Journal of Geophysical Research: Space Physics

Global and regional trends in ionospheric total electron content

Authors


Abstract

[1] A statistically significant positive trend of 0.6 ± 0.3 total electron content unit (TECU; 1 TECU = 1016 el m−2) per decade is detected in the 15 year record of daily averaged global total electron content obtained from multiple GPS observations between 1995 and 2010. The trend is extracted using a multiple regression analysis that simultaneously accounts for the comparatively larger global ionospheric responses to solar irradiance variability, solar-modulated annual and semiannual ionospheric oscillations, and geomagnetic activity. Geographical maps of regional trends in total electron content reveal both positive and negative local secular change during the past 15 years, with an overall larger increase in the Northern Hemisphere than in the Southern Hemisphere. Largest regional changes of as much as ±3 TECU per decade occur in the vicinity of 60°W to 60°E longitude and 15°S to 30°N latitude. TEC trend magnitude depends sensitively on the specification of solar EUV irradiance variations in the multiple regression model. The +0.6 TECU per decade trend pertains to equal solar irradiance levels during the 1996 and 2008 solar activity minima. When the specified solar irradiance is 15% lower in 2008 than in 1996, the derived global ionospheric trend increases to 3 TECU per decade. We contend that such a large global trend is implausible and that the associated anomalously low level of EUV irradiance in cycle 2008 minimum, reported in earlier publications, is unlikely to be real.

1. Introduction

[2] This paper presents an empirical analysis of recent trends in the total electron content (TEC) of Earth's ionosphere. Secular change in Earth's upper ionosphere has proven difficult to detect and the amplitude and sign of actual changes are uncertain, even though long-term trends are apparent in Earth's neutral upper atmosphere and lower ionosphere [Laštovička et al., 2008]. A decrease of 2.7 ± 0.5% per decade is evident in mass density at 400 km over the 40 years from 1967 to 2007, obtained from the analyses of the orbits of thousands of Earth-orbiting spacecraft [Emmert et al., 2008]. This trend is consistent with the expectation that the increasing concentration of greenhouse gases in Earth's lower atmosphere, which warms the surface and troposphere, is cooling the upper atmosphere, causing thermospheric density to decrease at fixed altitudes [Roble and Dickinson, 1989; Rishbeth and Roble, 1992].

[3] Simulations made with physical models of the thermosphere-ionosphere system suggest that over time the ionosphere will sink as the thermosphere cools and contracts in response to increasing greenhouse gas concentrations [Rishbeth and Roble, 1992; Bremer et al., 2004, Qian et al., 2008]. Changes in the peak electron concentration are predicted to be small to negligible, with electron number density decreasing above the peak (in the topside F2 layer, where two thirds of the total electron density resides) and bottomside concentrations increasing (in the F1 and E layers, where one third of the total electron density resides).

[4] Detection of the anticipated secular change is difficult and is expected to be challenging because the predicted decadal trends in both thermospheric and ionospheric densities are an order of magnitude smaller than the natural variations induced by solar cycle changes in extreme ultraviolet (EUV) irradiance. For example, the 2.7% per decade secular decrease in global mass density near 400 km is three orders of magnitude smaller than the ∼1000% increase from the minimum to the maximum of the 11 year solar activity cycle. Peak ionospheric electron concentrations increase by an order of magnitude [Liu et al., 2006] and total electron content by a factor of 5 during the solar cycle.

[5] Long-term secular change in ionospheric total electron content has not yet been investigated and presents an even greater detection challenge since it is expected to reflect the net effect of the purported small topside electron density decreases and bottomside electron density increases. Theoretical and experimental ionospheric trends have thus far been determined only for layer parameters, such as E and F peak heights, peak densities and critical frequencies, measured by ground-based ionosondes and radars. Extensive databases of the height and concentration of the layer's peak and of ion temperatures are interpreted typically in terms of background (mainly day to day) variability, solar activity (using the solar 10.7 cm radio flux, F10.7) and geomagnetic activity (using the geomagnetic index, Ap), each a function of local time, height and season [Zhang and Holt, 2008; Holt and Zhang, 2008]. Such trend studies are necessarily limited because global coverage is incomplete (especially in the Southern Hemisphere), regional variability can be significant, and the adopted relationships of the various ionospheric parameters and the removal of solar and geomagnetic effects vary among different analyses [Bremer et al., 2004; Laštovička et al., 2006; Jarvis, 2009].

[6] Trends in the peak height (hmF2) and concentration (NmF2) of the F2 layer (250–500 km) averaged over 50 ionosonde stations with more than 30 years of data are small with large uncertainties and depend on how the solar influence is eliminated [Bremer et al., 2004]. The trend in the height of the peak is −0.2 km per decade and the mean trend in critical frequency is ΔfoF2 = −0.02 MHz per decade. Regional trends, which may be larger, also remain poorly defined by ground-based observations, aside from a few comparisons of hmF2 at selected longitudes identifying a significant east-west gradient over Europe [Jarvis, 2009].

[7] Recent decadal trends in the lower ionosphere, at altitudes below that of the peak concentration, are somewhat more definitive, but still have significant uncertainties. Both the F1 (120–220 km) and E (90–120 km) ionospheric layers are decreasing in altitude (at a rate of 0.3 km per decade) and their peak concentrations are increasing [Bremer, 2008; Laštovička et al., 2008]. Trends in critical frequency derived from multidecadal time series from ionosondes over Europe are ΔfoF1 = +0.02 MHz per decade and ΔfoE = +0.013 MHz per decade.

[8] Here we analyze a new ionospheric database of total electron content constructed by the International GNSS Service (IGS) from space-based GPS measurements. With unprecedented homogeneity, global spatial coverage and 2 hourly temporal cadence, the IGS GPS-derived TEC database affords a unique global and regional perspective of ionospheric climatology during the past 15 years. We statistically identify and characterize the sources of variability in daily averaged TEC and develop an empirical model that accounts for ionospheric responses to varying solar electromagnetic and geomagnetic activity, oscillations at four periods and a long-term trend. We use this model to evaluate secular change in both the global total electron content and in different geographical regions, and to assess the sensitivity of the derived trends to three different scenarios of the solar EUV irradiance variations that are the dominant influence on ionospheric climatology.

2. Total Electron Content Variability

2.1. Observations

[9] A database of total electron content geographical maps constructed by the International Global Navigation Satellite Systems Service (IGS) Ionosphere Working Group from Global Positioning Satellite (GPS) data at 2 hour intervals since mid-1998 is the officially recognized IGS TEC data product [Hernández-Pajares et al., 2009]. Each IGS map is a weighted mean of maps produced at four GPS analysis centers: the Center for Orbit Determination in Europe (CODE), at the University of Berne, Switzerland; the European Space Operations Centre Ionosphere Monitoring Facility in Darmstadt, Germany; the Ionospheric and Atmospheric Remote Sensing Group at JPL, Pasadena, USA; and the Research Group of Astronomy and Geomatics, Technical University of Catalonia (UPC) in Spain. The weighting scheme relies on weekly comparisons of the Slant TEC (STEC) for a small set of permanent IGS stations and on the results of external self-consistency validations. TOPEX altimeter data provide routine validation of the TEC maps after July 2001.

[10] The daily averaged global TEC time series shown in Figure 1 (top) is obtained by summing over the 72 (longitude) × 71 (latitude) bins of each 2 hour IGS TEC map, accounting for the (cosine latitude) area factor, and then averaging over all available maps within each 24 hour (UT) period. Prior to 1998 the global TEC daily mean time series is extended using the zero-order term from the CODE database, which is available since 1995. As the map (in geographic coordinates) in Figure 1 (bottom) shows, the average ionosphere for 1998 to 2009 (for which TEC = 22.5 TECU) has the largest electron content at lower magnetic latitudes and closely tracks the magnetic equator, with local maxima at low latitudes both north and south of the magnetic equator and largest regional values at low northern latitudes over the Pacific Ocean.

Figure 1.

(top) Time series of daily averaged global total electron content (TEC), with the dashed line indicating the minimum TEC level and the dotted line indicating the average TEC for the period 1998–2009. (bottom) Geographical distribution of TEC for the average ionosphere (1998–2009), with the dashed line indicating the magnetic dipole equator. The corresponding zonal mean TEC is also shown, obtained both with (green curve) and without (red curve) the cosine correction for latitude area.

2.2. Empirical Model

[11] A model representation of the daily, global ionospheric TEC is constructed following J. L. Lean et al. (Ionospheric electron content: Global and hemispheric climatology, submitted to Journal of Geophysical Research, 2011) by adding to the baseline (minimum) ionosphere, TEC0, variations arising from solar activity, ΔTECsol, internal oscillations, ΔTECosc, geomagnetic activity, ΔTECgeo, and a secular trend, ΔTECtrend, such that

equation image

The baseline total electron content is TEC0 = 7.95 TECU, shown by the dashed black line in Figure 1 (top). The solar-driven component, ΔTECsol(t), at time t, is specified by the increase in solar EUV radiation above its minimum level, Emin, at lag τ1, and a (time-centered) 81 day smoothed term, E81, at lag τ2, according to

equation image

where E81min is the value of the 81 day smoothed time series at solar minimum and τ1 = 1 and τ2 = 1 day. The lag of one day is chosen because the cross correlation of daily TEC and solar EUV irradiance peaks at 1 to 2 days. Following Emmert and Picone [2010, section 5.2] the irradiance is specified at 1 AU; the annual oscillation term described below accommodates TEC variations attributable to the varying Sun-Earth distance of ±3.5% annually.

[12] Models must be used to reconstruct the solar EUV irradiance during the past 15 years in order to interpret TEC variability, because continuous solar EUV irradiance measurements from space commenced only in 2002 with the Solar EUV Experiment (SEE) on the Thermosphere Ionosphere Mesosphere Energetic and Dynamics (TIMED) spacecraft [Woods et al., 2005]. Three different time series of E, the solar EUV irradiance summed from 0 to 103 nm (the primary energy source for the global ionosphere), are shown in Figure 2 with dashed lines indicating their respective daily minimum values, Emin. The solar EUV irradiance model designated 3C in Figure 2a is constructed by empirically relating the SEE observations in each 1 nm wavelength band to the daily and 81 day smoothed Mg II and F10.7 indices [Lean et al., 2011]. The model designated SEM adds a secular irradiance trend to track the broad band monitoring of the Solar EUV Monitor (SEM) on the Solar Heliospheric Observatory (SOHO) since 1995 [Judge et al., 1998]. This trend is obtained by fitting the ratio of the SEM (26–34 nm) data to the 3C total EUV irradiance with a fifth-order polynomial in time. The fitted trend consists of a slight increase from 1996 to 1999, and a steady decrease thereafter. A third scenario, the 2C model [Lean et al., 2011], shown in Figure 2c, adopts a conservative approach to prescribing solar cycle EUV irradiance variations by accounting only for those changes directly indicated by the indices. The 2C model utilizes wavelength-dependent combinations of the Mg II and F10.7 indices of solar activity to reproduce the observed rotational modulation (alone). The solar cycle variations in the 2C model are determined by the long-term variations in the two indices, and are smaller in amplitude than in the 3C model.

Figure 2.

Compared are three different scenarios for the variation in the total EUV irradiance (0–103 nm) that produces the ionosphere during the epoch of the TEC observations in Figure 1. (a) The 3C model matches the direct observations made by the SEE on TIMED; (b) the SEM model matches the observations made by the SEM instrument on SOHO (the scaled zero-order channel) by imposing a secular irradiance trend on the 3C model; and (c) the 2C model reproduces the solar rotational modulation observed by SEE but with solar cycle changes inferred from the Mg II and F10.7 solar activity proxies. The dashed lines indicate minimum daily values during the 1996 solar activity minimum, and the gray points in Figures 2a and 2b are the residuals of the SEE and SEM observations, respectively, relative to the irradiance variability models.

[13] Four oscillations with periods p = 182.6, 365.25, 121.7 and 730.5 days are specified as combinations of baseline (invariant) and solar-modulated amplitudes

equation image

where the sine and cosine terms permit determination of both the phase and amplitude of each oscillation, and the collective amplitude modulation is prescribed as a linear function of the (time-centered) 81 day smoothed solar EUV irradiance. The periods 182.5 and 365.26 days correspond to the semiannual oscillation (SAO) and annual oscillation (AO), the two largest peaks in the periodogram of daily averaged global TEC; the periods 121.7 and 730.5 days correspond to a terannual oscillation (TO) and a biennial oscillation (BO) that are present in the residuals of the TEC data and an initial model constructed with only the SAO and AO cycles (see Lean et al., submitted manuscript, 2011).

[14] The geomagnetic component is represented by daily mean values of the Ap index obtained from the United States National Geophysical Data Center, lagged at τ3 = 1 day (the lag for which the cross correlation of daily TEC and Ap peaks), by

equation image

and the linear trend term is

equation image

Using multiple linear regression to obtain TEC0 and the coefficients a1–20 of each of the 20 time series (including the trend) that permit the best match of the observed TEC, the resultant model accounts for 98% of the IGS global TEC variance (the correlation coefficient of the observations and model is 0.993 using either the 3C or 2C EUV models and 0.986 using the SEM model). According to the standard multiple regression estimates, σstd, of the parameter uncertainties (which assume that the data–model random errors are independent and identically distributed), all terms (including the trend term) are significant; the σstd values are of order 10% of the parameter values or less.

[15] The ability of the empirical model of global TEC variability to capture more than 98% of the variance in 15 years of daily averaged TEC observations by combining solar, oscillatory, geomagnetic, and trend components is evident in the close agreement of the modeled and observed time series in Figures 3, 4, and 5, which use the 3C, SEM, and 2C EUV irradiance models, respectively (i.e., Figures 2a, 2b, and 2c). In all cases the modeled TEC deviates only minimally from that observed; the data-model residuals are shown as the gray lines in Figures 3a, 4a, and 5a. When the 3C and 2C EUV irradiance models are specified in the regression analysis the standard deviation of the residuals is 1.4 TECU, but using the SEM-like irradiance model the standard deviation of the residuals is larger, 1.9 TECU. Lean et al. (submitted manuscript, 2011) provide additional details of the TEC empirical model and interpretation of the individual solar, geomagnetic and oscillatory components.

Figure 3.

Compared are (a) the daily averaged global mean TEC (black line from Figure 1) with a model (green line) that combines the individual influences of (b) daily and smoothed solar irradiance specified by the 3C model and geomagnetic activity; (c) annual, semiannual, terannual, and biennial oscillations; and (d) a linear trend. The gray points in Figure 3a are the residuals of the TEC observations around the full model, and the gray points in Figure 3d are the residuals around the model with the trend term excluded.

Figure 4.

Compared are (a) the daily averaged global mean TEC (black line from Figure 1) with a model (green line) that combines the individual influences of (b) daily and smoothed solar irradiance specified by the SEM model and geomagnetic activity; (c) annual, semiannual, terannual, and biennial oscillations; and (d) a linear trend. The gray points in Figure 4a are the residuals of the TEC observations around the full model, and the gray points in Figure 4d are the residuals around the model with the trend term excluded.

Figure 5.

Compared are (a) the daily averaged global mean TEC (black line from Figure 1) with a model (green line) that combines the individual influences of (b) daily and smoothed solar irradiance specified by the 2C model and geomagnetic activity; (c) annual, semiannual, terannual, and biennial oscillations; and (d) a linear trend. The gray points in Figure 5a are the residuals of the TEC observations around the full model, and the gray points in Figure 5d are the residuals around the model with the trend term excluded.

3. TEC Trends

3.1. Global Trends

[16] The trend coefficients (a20 in equation (5)) obtained from the multiple regression analysis using the 3C, SEM, and 2C EUV irradiance variability models (Figures 3, 4, and 5) are 0.45, 3.2, and 0.74 TECU per decade, respectively, with σstd uncertainties of order 10%, as listed in Table 1. Relative to the average TEC value over this entire period of 22.5 TECU (dashed line in Figure 1), the corresponding trends are 2%, 14% and 3% per decade. It is difficult to authenticate a small secular trend of order a few percent per decade in just 15 years of global TEC whose variations are a factor of 5 during the canonical 11 year solar cycle (cycle 23 was ∼12 years); actual uncertainties are undoubtedly larger than implied by the σstd values (J. T. Emmert and J. M. Picone, Statistical uncertainty of thermospheric density trends derived from orbital drag, submitted to Journal of Geophysical Research, 2011), as shown below.

Table 1. TEC Trends and Uncertainties Obtained With Different Specifications of Solar EUV Irradiance Variability, Using Different Techniques, and Compared With the Theoretical Change Due to Increasing Greenhouse Gas Concentrationsa
Solar EUV IrradianceMultiple Regression Model Using ∼5500 Daily Mean Global TEC Values (a20 ± σstd)Average of 20 Multiple Regression Fits to ∼550 Randomly Selected Values (a20 ± σSS)Analysis of Residuals Accounting for Autocorrelation (a20 ± σAC)
The 3C EUV model0.45 ± 0.040.44 ± 0.10.4 ± 0.3
SEM EUV model3.2 ± 0.063.1 ± 0.22.2 to 3.1 ± 0.6 to1.0
The 2C EUV model0.74 ± 0.040.78 ± 0.10.7 ± 0.2 to 0.4
The 3C and 2C model average  0.6 ± 0.3
Theoretical anthropogenic trend  −0.15

[17] To assess robustness of the TEC trends shown in Figures 3d, 4d, and 5d we undertake a variety of tests and alternative analyses. As a test for the stability of the regression model, the coefficients are calculated for different subsets of days randomly selected from the entire database. The multiple regression model of TEC variability and the trend magnitudes are essentially invariant whether determined by the coefficients obtained from a single regression using all days (∼5500) of the database or from the average coefficients obtained from repeated regressions of different (randomly selected) subsets of the database. The example of this analysis provided in Table 1 is for 20 realizations of the multiple regression model, each with ∼10% of the available daily mean data. The uncertainties, σSS (the average of the uncertainties of the subset trends), are about a factor of two to three larger (as expected for a 10% sample) than the σstd uncertainties of the trend regressions coefficients obtained using the full data set.

[18] Multiple regression estimates of trend uncertainties assume independent random errors in the data, a requirement that is rarely fulfilled in upper atmospheric time series (Emmert and Picone, submitted manuscript, 2011). When the trends are estimated taking into account autocorrelation in the residuals (using the approach of Emmert and Picone (submitted manuscript, 2011)) the trend magnitudes, also listed in Table 1, are equivalent to those derived from the multiple regression model but the estimated uncertainties, σAC, are a factor of five to ten larger. In this case the trends obtained when specifying either the 3C or 2C model representation of solar EUV irradiance variability in the multiple regression analysis are not significantly different. We therefore adopt 0.6 ± 0.3 TECU per decade as the most likely trend magnitude and its uncertainty on the basis of the average of the trends computed using the 3C and 2C EUV models. We exclude the much larger 3.2 TECU per decade trend obtained with the SEM EUV irradiance variations, since we consider such a large trend in total electron content implausible, as discussed below.

[19] How the length of a time series affects the magnitude of a derived trend can also provide insight as to the veracity of that trend [Laštovička et al., 2008]. Specifically, the convergence of trend magnitude as a data set increases in length implies that the time series is sufficiently long for the derived trend to be valid. Figure 6 illustrates the dependence of trend magnitude on the length of the data set used to evaluate the multiple regression model coefficients. This dependence is obtained by selecting different subsets of the TEC daily mean database in two different ways. In Figure 6a the length of the data set extends forward in time from 1995 (solar minimum) whereas in Figure 6b the length of the data set extends backward in time from 2010 (also solar minimum). That the trend magnitude converges as the data set increases in length from 2003 to 2010 (after 1995; see Figure 6a) and extends back in time from 2002 to 1995 (before 2010; see Figure 6b) suggests that the extraction of a meaningful trend is possible from the 15 years of daily mean global TEC.

Figure 6.

The dependence of the TEC trend on the length of the data set is shown for the regression models using both the 3C and 2C EUV irradiance variability models. (a) Trends for epochs of increasing length starting in 1995 and (b) trends for epochs of decreasing length ending in 2010. Also shown (red symbols) are the trends for selected epochs estimated by taking into account the autocorrelation of the residuals, with error bars indicating ±σAC.

3.2. Regional Trends

[20] Both observational analysis of ground-based ionosondes [Jarvis, 2009] and recent model simulations [Qian et al., 2009] suggest that ionospheric trends are not geographically uniform. To characterize the regional dependence of the TEC trends we construct multiple regression models (equation (1)) for each 5° × 2.5° longitude-latitude bin of the 72 (longitude) × 71 (latitude) array, using daily mean TEC maps obtained by averaging the 2 hourly IGS maps. Local 1998–2010 TEC trends, normalized to the estimated global 1995–2010 trend of 0.6 TECU per decade, are shown in Figure 7a as absolute TEC values (in TECU) and in Figure 7b as percentage changes relative to the average TEC map (Figure 1, bottom). As with the global trends, regional trend amplitudes are very sensitive to the EUV irradiance time series used in the regression analysis; however, the regional pattern of TEC trends is essentially invariant with respect to the EUV specification.

Figure 7.

(a) The geographical distribution of 1998–2010 TEC trends obtained using the 3C model of EUV irradiance variability as absolute values in TEC units. The trend values have been normalized so that the global mean trend is +0.6 TECU per decade (the average of the 1995–2010 global trends using the 2C and 3C models). (b) Percentage changes relative to the average ionosphere in Figure 1 (bottom). Also shown are the respective zonal means determined with and without cosine weighting of latitude.

[21] Evident in Figure 7 is a strong association of ionospheric trend magnitude with Earth's magnetic field; zonal bands of alternating stronger and weaker TEC trends approximately parallel the magnetic dipole equator. Within the bands are wave-like fluctuations in TEC trend strength. Regionally, the TEC trends are largest where the dipole and dip equators diverge. Positive TEC trends in excess of +3 TECU per decade are located over the eastern Atlantic Ocean and western Africa in the midlatitude Northern Hemisphere; negative trends in excess of −3 TECU per decade occur over South America and equatorial Atlantic and Africa, between the magnetic and dip equators. Zonal average trends, also shown in Figure 7, are positive at all latitudes except near the South Pole. Trends in northern midlatitudes are larger (percentage wise) over the USA and Europe (longitude 180°W to 60°E) than over Eurasia (longitude 60°E to 180°E).

3.3. Inferred Vertical Profiles

[22] Since there are no estimates thus far of long-term trends in TEC, we assess the compatibility of our derived trend in daily averaged global TEC of +0.6 ± 0.3 TECU per decade with available estimates of ionospheric secular change by exploring plausible vertical profile changes that could compose the TEC trend. For this purpose we use the International Reference Ionosphere model (IRI2007; see Bilitza et al. [2006]) to construct a typical daily averaged global electron density profile (actually the daily global mean on 1 January 2000) shown in Figure 8a. The peak concentration is NmF2 = 7 × 1011 electrons m−3 at hmF2 = 350 km and the TEC is 22.6 TECU, consistent with the average value of TEC for the entire IGS database (dashed line in Figure 1). For this profile, two thirds of the total electron content (14.5 TECU) resides about the peak, in the F2 layer.

Figure 8.

(a) A representative daily averaged electron density profile, determined from the IRI2007 model and compared with the profile calculated by a 1-D model [Qian et al., 2008]. (b) Scenarios for trends in the electron density profile. For the three trend profiles shown in blue, the corresponding TEC trend is 0.6 TECU. The theoretical trend from increasing concentrations of greenhouse gases shown in red (from the 2 × CO2, or 2000–2100, simulation of Qian et al. [2008] interpolated to a single decade) produces a decadal TEC change of −0.15 TECU.

[23] We focus on reported changes in electron density concentration (not layer height) because we expect that TEC, a measure of the integrated electron density at all altitudes, is less sensitive to vertical shifts in ionospheric layers than to layer concentrations. One possible explanation of the +0.6 TECU per decade trend for the period 1995 to 2010 is a systematic positive increase of 2.7% per decade (relative to 22.5 TECU) at all altitudes; that is, simultaneously in the F2, F1 and E layers. The thick line in Figure 8b illustrates such a perturbation to the electron density profile in Figure 8a.

[24] Ground-based observations indicate, however, that on longer time scales upper ionospheric concentration is decreasing, not increasing. The trend in foF2 from observations at 50 ionosonde stations prior to 2005 is ΔfoF2 = −0.01 MHz per decade [Bremer et al., 2004], which is equivalent to a few tenths percent per decade decrease in peak electron concentration (assuming NmF2 = 1.24 × 1010foF22 = 7.5 × 1011 electrons m−3, foF2 = 7.8 MHz). Theoretical simulations further suggest that the ionospheric response to increasing greenhouse gas concentrations is a decrease in topside electron densities. A steady state 1-D global mean simulation of representative electron density profiles in 2000 and 2100 suggests a decrease of 2% per decade in electron concentrations above the profile peak, with only small changes in the peak concentrations [Qian et al., 2008].

[25] To explore electron density profile changes compatible with both our derived positive trend in daily averaged global mean TEC from 1995 to 2010 and negative topside ionospheric trends indicated by ground-based observations and theoretical simulations, we illustrate in Figure 8b two additional perturbations of the IRI electron density profile (Figure 8a) in which topside electron density changes (above 450 km) are arbitrarily constrained to zero and −2%, with no change in concentration at the peak (350 km). Because only one third of the total electron density resides below the profile peak, relatively large increases in bottomside densities (below 250 km) are needed to produce a positive 0.6 TECU change when topside concentrations are thus constrained to be unchanging or decreasing at 2% per decade. The resulting trends of +13% and +18% per decade are shown in Figure 8b (dashed and thin solid lines).

[26] The inferred increases of +13% and +18% per decade in lower ionospheric electron densities are an order of magnitude larger than the theoretical +1.5% per decade increase that Qian et al. [2008] simulate for the influence of greenhouse gases on this region (also shown in Figure 8b) and are larger also than the concentration changes obtained experimentally from the critical frequency trends. With NmF1 = 1.24 × 1010foF12 = 2.5 × 1011 electrons m−3, the F1 critical frequency trend of ΔfoF1 = +0.02 MHz per decade obtained by Bremer [2008] corresponds to a trend in the F1 peak electron concentration of ΔNm F1 = +0.9% per decade. With NmE = 1.24 × 1010foE2 = 5.5 × 1010 electrons m−3 the E region critical frequency trend of ΔfoE = +0.013 MHz per decade corresponds to a peak E region concentration trend of ΔNmE = +1.2% per decade. Of course, profile changes other than the three we have chosen are possible; our examples simply illustrate the difficulty in reconciling the observed TEC secular change from 1995 to 2010 inferred from the IGS databases with either ionosonde-based or model-based trend estimates on longer time scales.

4. Discussion

[27] The positive trend of +0.6 TECU per decade that we detect in daily averaged global TEC during the past 15 years is significant and accompanied by a distinct regional pattern of both positive and negative trends organized by magnetic latitude. We examine the likelihood that the derived TEC trend represents real change in the ionosphere, as opposed to artifacts of the observational TEC database or our analysis.

[28] Clearly the calibration fidelity of the long-term IGS TEC maps is crucial for the extraction of a reliable long-term trend. As the official product of the International GNSS Service (IGS) working Group on Ionosphere, the IGS TEC maps have been tested and validated and are considered superior to any of the databases of TEC maps from individual centers [Hernández-Pajares et al., 2009]. Nevertheless, small biases are evident among the maps from individual centers, for example as a result of technique updates, so spurious long-term trends in the IGS TEC map calibrations cannot be excluded. It is possible, also, that the extension of the global IGS TEC time series prior to 1998 with the CODE TEC values may contribute a spurious trend, even though the correlation of the IGS and CODE daily averaged global mean time series is high (0.998 for 4143 common values between 1998 and 2010).

[29] Even small uncertainties in the proxy-based models of solar EUV irradiance may also produce spurious TEC trends, since the magnitude of the derived trend depends sensitively on the adopted irradiance time series used to model the solar–induced and oscillatory variations in the TEC global time series. That the estimated statistical uncertainties (with or without taking into account autocorrelation) are smaller than the difference in the trend estimates caused by the choice of EUV model suggests that the uncertainty in specifying true solar EUV irradiance variability may currently be the more important source of error. Although our model of daily averaged global TEC accounts for more than 98% of the observed variance, there is nevertheless structure present in the residuals, which suggests that further improvements are possible. Residual variance is larger during higher solar activity (thus violating the assumption of identically distributed random error) and exhibits autocorrelation near 27 days. This suggests that our regression model does not fully capture the modulation of TEC imposed by the Sun's rotational modulation of the EUV irradiance, which is negligible during solar minimum and as much as 15 TECU during solar maximum (Lean et al., submitted manuscript, 2011).

[30] Even were the TEC database, the EUV irradiance time series and the regression model free of error, a 15 year epoch itself challenges reliable trend detection because of uncertainties in representing just one realization of the ionosphere's response to the dominant source of variability, the 11 year solar EUV irradiance cycle [Weatherhead et al., 2002]. For example, systematic cycle-to-cycle differences are evident in thermospheric chemistry (and hence the ionospheric plasma density) that affect F2 layer response to geomagnetic storms [Rishbeth and Field, 1997]. The temporal coverage of the database is too limited even to quantify autocorrelation in the residuals at a lag of 11 years, the dominant TEC cycle, even though there is a clear increase in residual magnitude during solar activity maximum. That the trend magnitude appears to converge as the data set increases in length from 2007 to 2010 (after 1995; see Figure 6a) is consistent with a meaningful trend, but alternatively this apparent trend stability may simply reflect minimal TEC variability owing to very low solar activity in these most recent years.

[31] Assuming that the inferred trend in daily averaged global mean TEC of +0.6 TECU per decade is accurate for the period 1995 to 2010, its origin is unclear. The TEC change corresponding to the electron density profile changes that Qian et al. [2008] simulated (Figure 8b) using a single column (1-D) model is −0.15 TECU per decade, a factor of 4 smaller in magnitude and opposite in sign to our experimental trend. In the lower ionosphere, electron concentration changes compatible with a +0.6 TECU per decade trend (assuming changes of −2% per decade to zero in the upper ionosphere) exceed significantly the secular trends inferred from ground-based ionosonde F1 and E region data over the past 30–50 years or expected theoretically from ionospheric responses to increasing concentrations of greenhouse gases. However, the theoretical estimates may underestimate electron concentration increase in the lower ionosphere [Laštovička et al., 2008].

[32] Although the positive global TEC trend that we obtain from the IGS data is opposite in sign and larger in magnitude than model simulations of ionospheric responses to greenhouse gas increases, the regional pattern of relative TEC trend magnitude (Figure 7) is consistent with the model indication that hmF2 and NmF2 trends correlate with the magnetic dip equator [Qian et al., 2009] and with evidence for longitudinal gradients. Our pattern of TEC trends shows a large-scale structure in the middle- and high-latitude Northern Hemisphere, with larger TEC trends at 3°W than at 104°E. This longitudinal pattern may be related to the decrease in altitude of the F region ionosphere from 3°W to 104°E that Jarvis [2009] detects in ground-based data, and speculates to be associated with a large-scale wavelike feature. Given the dependence of the TEC trend on geomagnetic coordinates and time of day, the single profile model of Qian et al. [2008] may well not represent our daily averaged global trend very well.

[33] There is evidence for recent anomalous behavior in the upper atmosphere [Emmert et al., 2010] that may account for larger than expected ionospheric change during the 15 year period from which we extract our TEC trend. The globally averaged mass density at 400 km decreased 29% in the 2008 solar minimum relative in the prior 1996 minimum, producing a trend over the 15 years from 1995 to 2009 (inclusive) of −15.3 ± 4.5% per decade. This negative trend is almost 6 times larger than the secular decrease of −2.7 ± 0.5% per decade in 400 km thermospheric density over the 40 years from 1967 to 2007 [Emmert et al., 2008]. Starting in about 2005, neutral densities near 400 km began to diverge from the 40 year climatology and became increasing lower during the prolonged solar minimum period [Emmert et al., 2010]. We speculate that the positive 2.7% per decade TEC trend that we detect may be connected to the 15.3% per decade decline in thermospheric mass density during the past 15 years. The predicted and observed positive bottomside trends, which can be explained by a decrease in the NO+/O2+ ratio [Qian et al., 2008], may have been similarly magnified during this unusual period. It would be interesting to investigate how foE and foF1 have behaved since 2005.

[34] We consider the 3.2 TECU (14%) per decade trend in global TEC that we derive when specifying solar EUV irradiance variations according to the SEM observations, to be spurious and likely the result of sensitivity drifts in the SEM instrument. The positive relationship between global TEC and solar EUV irradiance is unequivocal, widely reported both during the 27 day solar rotation and the solar activity cycle [Liang et al., 2008; Afraimovich et al., 2008], and prominently reflected in our regression model of TEC variability (Figures 3b, 4b, and 5b). Were the EUV irradiance actually 15% lower in the 2008 minimum than in the 1996 minimum (as the SEM data indicate) then TEC densities would be lower, not higher, in 2008 relative to 1996. The large positive trend from the empirical model formulated with the SEM-based irradiance variability model (Figure 4d) simply compensates for the low solar-related TEC levels in 2008 (Figure 4b) that the (spurious) irradiance decline produces. A TEC trend of 3.2 TECU per decade implies implausibly large changes in the electron density profile; a 14% per decade increase if constant at all altitudes, or a 66% per decade increase in bottomside ionospheric electron densities if invariant at altitudes above the peak. These trends are sufficiently large to have been readily detected by ground-based ionosondes but no such trends have been reported. The inference from the TEC data that solar EUV irradiance levels were not 15% lower in 2008 than 1996 consequently invalidates the supposition that the thermospheric density anomaly in 2008 is ascribable solely to this (presumed) irradiance decrease [Solomon et al., 2010].

5. Summary

[35] There is a statistically significant trend of +0.6 ± 0.3 TECU per decade in daily averaged global TEC during the 15 years from 1995 to 2010. Accompanying the global trend is a regional pattern of larger, positive trends in two low-latitude bands paralleling the magnetic equator to the north and south. In the equatorial Atlantic region the trends are negative instead of positive. Trends are more strongly positive in the Northern Hemisphere than in the south, and stronger west of 40°E (over the middle- and high-latitude American continent, Atlantic Ocean and Europe) than over Eurasia.

[36] The period from 1995 to 2010, for which GPS-derived TEC data are available, includes a prolonged epoch of low solar activity in which thermospheric densities were anomalously low relative to the 40 year climatology prior to 2007. The average trend in 400 km mass density during this 15 year period is −15.3% per decade, which is significantly larger than the trend of −2.7% per decade from 1967 to 2007. The positive TEC trend of 0.6 TECU per decade and the negative 15.3% per decade mass density trend are consistent with a cooler thermosphere embodying a sunken ionosphere accompanied by bottom side electron density increases. Alternatively, the TEC increase may simply reflect reduced recombination rates under cooler thermosphere conditions or possibly a change in forcing from the lower atmosphere.

[37] The magnitude of the derived TEC trend (but not the qualitative regional pattern) depends sensitively on the adopted solar EUV irradiance, which produces the overall TEC increase during the solar cycle, drives shorter-term 27 day fluctuations and modulates the semiannual, and annual oscillations. Using an EUV irradiance time series in which levels during the 2008 minimum are 15% lower than in the 1996 minimum (as suggested by the SEM observations) produces a trend of 3.2 TECU per decade, five times larger than the 0.6 TECU per decade trend obtained when solar EUV irradiance is equal during the 1996 and 2008 minima. On the basis of comparisons of plausible electron density profile changes, we interpret the larger trend as an unrealistic artifact that compensates for low TEC values associated with the low SEM irradiances in the multiple regression analysis. We suggest that the SEM behavior does not represent true solar EUV irradiance changes in 2008 relative to 1996 and that, contrary to Solomon et al. [2010], the anomalously low thermospheric densities in 2008 are not directly solar driven.

[38] Future prospects favor increasingly reliable specification of TEC trends. The IGS TEC database continues to lengthen and its stability increases as the algorithms are revised and improved. New observations of solar EUV irradiance being made by the EUV Variability Experiment (EVE) on the Solar Dynamics Observatory [Woods et al., 2010] are extending the extant TIMED/SEE and SOHO/SEM observations and will help clarify the nature of EUV irradiance variability. Improved empirical models of TEC variability that can account for more than 98% of the variance (with residuals less than 1.4 TECU) are possible (and under development), taking into account the autocorrelation structure in the data–model residuals. Also underway is further analysis to establish the diurnal and seasonal dependencies of the TEC trends.

[39] Interpreting the causes of ionospheric trends requires concurrent observations of the neutral thermosphere and ionosphere and their multiple sources of variability, both from above and below. Longer and more precise solar, atmospheric and ionospheric data sets will enable improved regression models and superior physical understanding of linked atmosphere-ionosphere variability, including of lower atmospheric influences on the ionosphere and thermosphere. A comprehensive program of accurate, focused, multidimensional physics-based simulations of the ionosphere-thermosphere system is needed to better understand the observed anomalously cool thermosphere during the recent solar minimum period, the related increase in global average TEC and its regional counterparts, and the disagreements among various ionospheric parameter trends (including our own work) and with the physics-based simulations.

Acknowledgments

[40] ONR and NASA funded this work.

[41] Robert Lysak thanks Martin Jarvis and another reviewer for their assistance in evaluating this paper.