We investigate the ionospheric response to solar Extreme
Ultraviolet (EUV) variations using different proxies, based on solar EUV
spectra observed from the Solar Extreme Ultraviolet Experiment (SEE) onboard
the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED)
satellite, the F10.7 index (solar irradiance at 10.7 cm), and the Bremen
composite Mg-II index during January 2003 to December 2016. The daily mean
solar proxies are compared with global mean Total Electron Content (GTEC)
values calculated from global IGS TEC maps. The preliminary analysis shows a
significant correlation between GTEC and both the integrated flux from SEE
and the Mg II index, while F10.7 correlates less strongly with GTEC. The
correlations of EUV proxies and GTEC at different time periods are presented.
An ionospheric delay in GTEC is observed at the 27 days solar rotation period
with the time scale of about

The ionospheric E and F regions are important layers of the Earth's
atmosphere (above

Due to unavailability of direct EUV measurements before the space age, the
variation in TEC is frequently compared against solar proxies, with the most
common one being the F10.7 index, which is the irradiance at a wavelength of
10.7 cm, usually given in solar flux units (sfu, 10

In recent years, direct solar EUV flux measurements are available from various satellites such as the Solar EUV Experiment (SEE) onboard the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite (Woods et al., 2000, 2005), and the Extreme Ultraviolet Variability Experiment (EVE) onboard the Solar Dynamics Observatory (SDO) (Woods et al., 2012; Pesnell et al., 2012). However, due to degradation of EUV measuring instruments solar proxies may be more suitable (BenMoussa et al., 2013), or repeated calibration is necessary. The availability of the direct EUV measurements provide an opportunity for comparing EUV with different solar proxies (e.g., Jacobi et al., 2016).

Various researchers had observed a delayed response of

In recent years numerical, empirical, and physics-based thermosphere/ionosphere models have been developed to characterize ionospheric dynamics. Among them are the Coupled Thermosphere Ionosphere Plasmasphere Electrodynamics (CTIPe, Fuller-Rowell and Rees, 1983; Millward et al., 2001; Codrescu et al., 2012), the International Reference Ionosphere (IRI, Rawer et al., 1978; Bilitza et al., 2011) and Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM, Roble et al., 1988). These models play an important role in upper atmospheric studies (e.g., Negrea et al., 2012; Fedrizzi et al., 2012). To simulate solar variability, models are frequently driven by proxies like F10.7 index or the Mg-II index. The F10.7 index is the most widely used index in upper atmosphere research to represent the solar variability due to the availability of continuous measurements since 1947 (Woods et al., 2005). The solar EUV variability can be better represented by the improved F10.7 index using 81 days running mean (e.g., Viereck et al., 2001; Liu et al., 2006). The CTIPe model uses a modified F10.7 index, which is the average of the previous day value of the F10.7 index and the average of the previous 41 days (Codrescu et al., 2012). Fitzmaurice et al. (2017) used the CTIPe model to understand the influence of solar activity on the ionosphere/thermosphere during the geomagnetic storm. They reported that solar activity has the greatest effect on model simulated TEC.

The main aim of the present study is to find out the correlation and time delay between GTEC and solar proxies based on data from January 2003 to December 2016. To derive the periodicities in GTEC and solar proxies, the wavelet coherence and cross-wavelet method have been utilized. Preliminary results of a CTIPe model experiment to estimate the delay at the solar rotation time scale will also be presented.

In this work, we use daily global TEC maps from the International GNSS
Service (IGS, Hernandez-Pajares et al., 2009) provided by NASA's CDDIS
(Noll, 2010) data archive service (CDDIS, 2017). Gridded global TEC data is
available at a time resolution of 2 h and on a spatial grid of

Temporal variations of normalized datasets of GTEC (blue), SEE-EUV flux (black), F10.7 index (red), and Mg-II index (magenta) during year 2003 to 2016. The curves are vertically offset each by 2.

The CTIPe model is a global, 3-D, time-dependent, physics-based numerical
model. It consists of four components, namely (a) a neutral thermosphere
model (Fuller-Rowell and Rees, 1980), (b) a mid- and high-latitude
ionosphere convection model (Quegan et al., 1982), (c) a plasmasphere and
low latitude ionosphere model (Millward et al., 1996), and (d) an
electrodynamics model (Richmond et al., 1992), which run simultaneously and
are fully coupled. The thermosphere model is solving the equation of
momentum, continuity, and energy to calculate global temperature, density,
wind components, and atmospheric neutral composition. The parameters
calculated from the thermosphere code are used to calculate production,
loss, and transport of plasma. The transport terms consider ExB drift and
interactions of ionised and neutral particles under the influence of the
magnetospheric electric field (Codrescu et al., 2012). In the high latitude
model, the atomic ions of

To study the long-term variations in GTEC and EUV proxies, datasets from 2003 to 2016 have been used. Figure 1 shows the normalized time series of GTEC, SEE EUV flux, the F10.7 index, and the MG-II index. All data has been normalized by subtracting the mean and dividing by the respective standard deviation. The data represent the decreasing and increasing parts of solar cycle 23 and 24, respectively. As the solar radiation plays a major role in the electron production, the correlation of GTEC with solar EUV or EUV proxies must be significant and is also correlated at the 27 days solar rotation period. Figure 2 shows the cross correlation between GTEC and (a) TIMED/SEE integrated EUV flux (left panel), and (b) F10.7 index (right panel) from 1 January 2003 to 31 December 2016. Since we do not consider the seasonal cycle here, a low-pass filter with a cut off period of three months was applied to the data before.

Figure 2 shows a strong correlation between normalized GTEC and integrated EUV
flux (black) with a maximum correlation coefficient of 0.90 and shows a
weaker correlation with the F10.7 index (red) with a maximum correlation
coefficient of 0.84. Also, we have analyzed the correlation between GTEC and
Mg-II index which shows a good correlation with a correlation coefficient of
0.89 (figure not shown). Jacobi et al. (2016) analyzed GTEC and SDO/EVE
integrated EUV flux data from 2011 to 2014 and they also found a good
correlation of about 0.89. Unglaub et al. (2011, 2012) have shown that the
GTEC is more strongly correlated with the EUV-TEC proxy than with the F10.7
index. Figure 2 shows a delay of

Cross-correlation of GTEC with SEE-EUV flux (black) and F10.7 index (red). Positive values denote GTEC lagging SEE-EUV or F10.7, respectively.

In order to investigate the oscillations in the time series of GTEC and all EUV proxies in more detail, the continuous wavelet transform (CWT) method has been applied. The cross wavelet transform is constructed using 2 CWTs, which shows common high energies of the two time series and relative phase (Grinsted et al., 2004). We have used a Morlet mother wavelet. Furthermore, the wavelet coherence method is used to calculate significant coherence using Monte Carlo methods (Grinsted et al., 2004). Wavelet coherence can be calculated using 2 CWTs which shows the local correlation between the time series. All data has been normalized by subtracting the mean and dividing by the respective standard deviation.

The cross wavelet spectra between GTEC and both SEE–EUV flux and F10.7 index are shown in Fig. 3a and b, respectively.

GTEC shows common high power with SEE-EUV flux and F10.7 at scales of 16–32 days during 2003 to 2005 and during 2009 to 2016. During those times when the coherence is significant, GTEC is in phase with SEE-EUV and F10.7. Much less power at the 27 days periodicity is observed from 2007 to 2009, which is the extended part of solar cycle 23.

The magnitude squared coherence of GTEC with SEE-EUV flux and the F10.7 index is shown in Fig. 3c and d, respectively. The coherence spectrum shows the time and period range where the two time series co-vary. As shown in both figures, a high correlation is observed at the 27 days periodicity. The magnitude squared coherence between GTEC and SEE flux is very high at 27 days periodicity, while GTEC and F10.7 behave less coherent. In comparison to the cross wavelet in Fig. 3a, b, wavelet coherence shows larger significant regions in Fig. 3c, d.

The CTIPe model has been used to simulate the ionospheric variability and to
estimate the ionospheric delay due to solar variability. The model was run
for 15 March 2013 conditions (Kp index

Figure 4b shows the zonal mean TEC simulated by the CTIPe model. The
global TEC distribution qualitatively reproduces real ionospheric
conditions, e.g. enhanced electron density near the equator due to the
fountain effect (Appleton, 1946; Hanson and Moffett, 1966; Sterling et al.,
1969). TEC varies according to the F10.7 index, but with a delay which can
be seen by comparing the TEC maximum with the one of F10.7 in Fig. 4a.
Figure 4c shows global mean values for the F10.7 index and the CTIPe TEC,
both normalized by subtracting the mean and dividing by the respective
standard deviation. A delay of about 1–2 days is observed. Figure 4d
shows the cross-correlation and thus the delay between the input F10.7 index
and TEC simulated by the CTIPe model. The delay introduced here may be due
to vertical transport processes or slow diffusion of atomic oxygen, which
has been suggested by Jakowski et al. (1991) as a possible process for the
ionospheric delay. In order to understand the possible delay mechanism in
the GTEC, the normalized modelled global mean atomic oxygen ion density
(GAOID) is shown in Fig. 5 (upper row) for different altitudes. The
corresponding cross correlations between the F10.7 index and GAOID are shown
in the lower panel. It is interesting to note that at pressure

To contribute to the understanding of the long-term ionospheric behaviour with respect to solar EUV variations we have analyzed data from 1 January 2003 to 31 December 2016. In this study, the strong correlation between GTEC and solar proxies has been observed at the 27 days solar rotation period. There is a particularly strong correlation between GTEC and integrated SEE-EUV flux and the Mg II index, while F10.7 correlates less strongly with TEC. We have also observed an ionospheric delay at the 27 days solar rotation period with the time scale of 1–2 days between GTEC and all the solar proxies considered, thereby confirming earlier results in the literature.

To gain more insight into the possible reasons for the delay, we have run
the CTIPe model for 27 days and varied the input F10.7 index artificially
while keeping all the other conditions constant. Preliminary results show
that the model qualitatively reproduces the observed ionospheric delay of

To conclude, in this first approach we have found that the CTIPe model is able to reproduce the observed ionospheric delay. The results, however, are only preliminary. In further studies with more realistic EUV changes, we will also analyse photodissociation and ionization processes of atomic oxygen, molecular oxygen, and molecular nitrogen in more detail to check the validity of the results by Jakowski et al. (1991). Furthermore, we will investigate the delay in the different ionospheric parameters on different timescales by varying various model components (dissociation, ionization) thereby investigating the physical processes responsible for the delay.

IGS TEC data has been provided via NASA through

CJ, RV, JB, ES, and MC designed the study. RV performed the CTIPe model run with help from MC and CJ. RV analysed the data. CJ together with RV drafted the first version of the text. All authors discussed the results and provided critical feedback and contributed to the final version of the manuscript.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2017”. It is a result of the Kleinheubacher Tagung 2017, Miltenberg, Germany, 25–27 September 2017

The study has been supported by Deutsche Forschungsgemeinschaft (DFG) through grants no. BE 5789/2-1 and JA 836/33-1. Edited by: Ralph Latteck Reviewed by: Matthias Förster and one anonymous referee