The ionospheric response to solar extreme ultraviolet (EUV) variability during 2011–2014 is shown by simple proxies based on Solar Dynamics Observatory/Extreme Ultraviolet Variability Experiment solar EUV spectra. The daily proxies are compared with global mean total electron content (TEC) computed from global TEC maps derived from Global Navigation Satellite System dual frequency measurements. They describe about 74 % of the intra-seasonal TEC variability. At time scales of the solar rotation up to about 40 days there is a time lag between EUV and TEC variability of about one day, with a tendency to increase for longer time scales.

The solar extreme ultraviolet (EUV) radiation varies on different time
scales, including the 27-day Carrington rotation as one of the primary
sources of variability at the intra-seasonal time scale. Consequences are
strong changes of the Total Electron Content (TEC), which is the vertically
integrated electron density of the ionosphere/plasmasphere systems, often
given in terms of TEC Units (TECU, 1 TECU

Parameters describing ionospheric electron density and EUV proxies are not
always in phase, and several studies report a delayed response of the
ionospheric plasma density to solar activity changes (e.g. Jakowski et al.,
1991; Astafyeva et al., 2008; Afraimovich et al., 2008; Lee et al., 2012).
In most cases, TEC is reported to be delayed against the variation of the
solar radiation by 1–2 days. To interpret the ionospheric delay, Jakowski et
al. (1991) performed simplified theoretical studies using a one-dimensional
numerical model, and found a delayed accumulation of atomic oxygen at 180 km
height, and this delay was due to slow diffusion of O that has been created
via O

Time series of daily integrated EUV fluxes (6–106 nm, red) from SDO/EVE and daily averaged global mean TEC (green).

In this paper, we shall make an attempt to analyze the ionospheric delay based on datasets that represent solar EUV variability. In particular, we will investigate the time lag at different time scales between about 2 weeks and 3 months. We shall use integrated EUV-fluxes from the Extreme Ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO), the EUV-TEC proxy based on the SDO/EVE spectra and the NRLMSISE-00 model (Picone et al., 2002). We shall use data from 2011 through early spring 2014, and analyze the correlation between EUV proxies and global TEC variability, as well as the ionospheric delay at different time scales.

SDO was launched on 11 February 2010 (Pesnell et al., 2012), and data are available from 1 May 2010. EVE onboard SDO measures the solar EUV irradiance from 0.1 to 106 nm with a spectral resolution of 0.1 nm, a temporal cadence of ten seconds, and an accuracy of 20 % (Woods et al., 2012). The in-flight calibration for EVE includes daily measurements with redundant foil filters and on-board flatfield lamps and annual underflight calibration rocket flights. Diode-based broadband channels are also used to monitor the performance and drift of the high-resolution spectrographs.

For comparison of EUV parameters with ionospheric variability, daily mean global mean TEC values have been calculated based on International Global Navigation Satellite System Service (IGS) TEC maps (Hernandez-Pajares et al., 2009) provided by CDDIS (2015), and they will be used here to analyze the correlation between ionospheric and EUV variability. Figure 1 shows the time series of daily integrated EUV fluxes together with global mean TEC. The data represent part of the increasing phase of solar cycle 24. Naturally, at the interannual time scale, the two curves are strongly correlated. Also, correlation is strong at the time scale of the 27-day solar rotation.

We calculate the EUV-TEC proxy after Unglaub et al. (2011, 2012), which
represents the vertically integrated ionization rates, and used SDO/EVE
version 5 spectra (LASP, 2015) between 6 and 106 nm as input. The far ultraviolet (FUV)
irradiance up to about 130 nm also contributes to ionization, but its
contribution is not included in the integrated EUV band because their
ionization contributions are primarily below the ionosphere F layer that is
most important for TEC. EUV-TEC is calculated from the satellite-borne EUV
measurements assuming a model atmosphere that consists of four major
atmospheric constituents. Regional number densities of the background
atmosphere are taken from the NRLMSISE-00 model (Picone et al., 2002). This
model uses the F10.7 flux as daily input, and additionally as 81-day mean.
Since the main input to EUV-TEC is the solar EUV, it is strongly correlated
to the integrated EUV flux. The correlation coefficient is

The original SDO/EVE spectra integrated from 6–106 nm and the EUV-TEC proxy are subsequently used for comparison with global TEC. Because the annual cycle of global TEC and ionization is different, especially owing to the semiannual cycle in TEC, we here consider the seasonal time scale up to 3 months only. Therefore the data have been high-pass filtered using a FFT filter with a cut-off period of 3 months.

To allow comparison, the datasets were normalized by subtracting the mean
and dividing by the standard deviation using the data from 16 March 2011
through 11 February 2014 (approx. Carrington rotations 2108–2146). The
mean values and standard deviations are

Figure 3 shows scatter plots of EUV-TEC (panel a), and SDO/EVE integrated spectral
flux (panel b) vs. daily mean global mean TEC. All the data have been high-pass
filtered and normalized as described above. The correlation coefficient
between normalized TEC and EUV-TEC is

Time series of EUV-TEC (black), SDO/EVE integrated flux (red) and daily averaged global mean TEC (green), filtered using a high-pass filter with cut-off period of 3 months and normalized by their mean and standard deviation. The curves are offset vertically with respect to each other.

Figure 4 shows Morlet wavelet spectra of SDO/EVE integrated EUV fluxes (left panel) and daily mean global mean TEC (right panel). Data have been normalized and low-pass filtered as in Fig. 2. The main variation is clearly near 27 days, but there is also some power at longer time scales, although this is only intermittent.

Figure 5 shows an example of time series of SDO/EVE integrated EUV fluxes and
global TEC, which have further been filtered using a Lanczos bandpass filter
with 100 weights and cut-off periods of 25 and 29 days, so that the time
series represents the respective variability within the 27-day solar cycle.
We note a delay of TEC with respect to solar variability. To systematically
investigate the delay at different time scales, we now filtered the time
series in different period bands, and the cut-off periods of the Lanczos
filter were chosen in such a way that each period band ranges over 4 days,
while the center of the period band was shifted from 4 to 88 days. For each
pair of filtered time series, i.e. for each time scale (which was defined as
the center of the respective period window), the cross-correlation
coefficients were calculated. The results are shown as contour lines in Fig.
6; the line with a cross correlation of

EUV-TEC

At first glance the difference in lag at time scales > 55 days
may contradict the strong correlation of integrated EUV fluxes and EUV-TEC,
However, at these time scales the correlation coefficients are still large
(between

Morlet wavelet spectra of

Example of normalized SDO/EVE integrated EUV fluxes and global mean TEC, additionally filtered in the 25–29 days period range.

Cross-correlation coefficients between filtered global TEC and
SDO/EVE integrated EUV fluxes. The time scale on the abscissa defines the
center of the 4-day period band of the respective filter. On the ordinate
the time lag is given in degrees, and 360

We show the same data in a different manner in Fig. 7. Now we show the ratio
of the correlation coefficients and the maximum correlation for the
respective time scale of the variations, which means that a horizontal
contour line would denote a constant decrease of correlation with the phase
of the respective variation. The light magenta region indicates the region
where the ratio exceeds 0.99. One can see that for the time scales of about
20–40 days this region is more or less constant (the fluctuations occur
because we have a time resolution of 1 day only) at about 15

As in Fig. 6, but shown is the ratio of the cross-correlation coefficient and the one at the lag of maximum correlation.

We have made an attempt to include the ionospheric delay shown in Figs. 6
and 7 into the EUV and EUV-TEC time series. The time series had been
filtered in the respective time ranges, the shifted by the delay (0–2 days),
and then the filtered series had been added up again. As expected, the
correlation increases, namely to

We analyzed the correlation between global mean TEC and solar EUV variability, the latter described by 2 different proxies, namely the integrated EUV flux measured by SDO/EVE, and the EUV-TEC proxy that describes primary ionization based on EUV spectra. There is an ionospheric delay at the solar rotation and longer time scale of 1–2 days, such that TEC variations lag EUV ones. There is some indication that this delay is constant when taken relative to the time scale of the EUV variations, i.e. increases slightly for variations from 20 to 40 days. For longer time scales up to 90 days, the relative delay decreases, but then remains constant again. We did not investigate time scales longer than 90 days.

It should, however, be stated here that the EUV fluxes and the ionization rates calculated by the EUV-TEC model represent only a coarse description of global TEC, and they are not well suited to describe ionization e.g. in circulation models. A parameterization of ionization and dissociation rates including photoelectron effects using solar spectral measurements or models has been presented by Solomon and Qian (2005). When used as a TEC proxy, EUV-TEC does not account for dynamics, secondary ionization, or ionization through particle precipitation. It does not take into account effects of ionospheric storms, which are a challenge for TEC forecast (Borries et al., 2015). Nevertheless, the integrated EUV flux or EUV-TEC describes TEC variations well, especially at the time scale of the solar rotation.

Obviously, the results presented here are preliminary. We used daily EUV spectra and daily and globally averaged TEC, which gives only coarse values for the ionospheric delay. Furthermore, F10.7 is observed at local noon and this may lead to a bias between F10.7 used in NRLMSISE-00 and daily TEC. TEC maps are available at higher temporal resolution, and EUV fluxes at least for some spectral bands are also available e.g. from the Solar and Heliospheric Observatory/Solar Extreme Ultraviolet Monitor (SOHO/SEM, Judge et al., 1998) or the Geostationary Operational Environmental Satellites (GOES). This provides the possibility to study ionospheric delay in higher temporal resolution and spatially resolved. However, for the calculation of the EUV-TEC index spectral resolution is required, so that this would only provide a guidance for further improvements. There are still some further shortcomings of EUV-TEC. One aspect is probably the use of F10.7 in the NRLMSISE-00 atmosphere model used, so that EUV-TEC in this version is based on EUV spectra and F10.7. First preliminary results using the EUV-TEC proxy including NRLMSISE-00 based on EUV fluxes showed slightly better correlation with TEC, however, still gave slightly weaker correlation than using EUV integrated fluxes alone.

As in Fig. 3, but with EUV-TEC and SDO/EVE integrated fluxes shifted according to the delay as shown in Figs. 6 and 7.

Another aspect is that we completely neglect the thermosphere and its dynamics in the analysis. If the delay should be caused by dynamical processes as suggested by Jakowski et al. (1991), it is at least partly driven by FUV radiation and therefore the spectra used here are not necessarily sufficient to describe the variability. Further analyses, therefore will take this in to account, e.g. by using the MgII index instead of EUV, or in a combination.

The EUV-TEC model can be obtained from the corresponding author on request.
The code includes the NRLMSIS-00 model provided by CCMC via

IGS gridded TEC data has been provided via NASA through

The original version of the EUV-TEC model has been written by C. Unglaub, Leipzig. We acknowledge support from the German Research Foundation (DFG) and Universität Leipzig within the program of Open Access Publishing. Edited by: M. Förster Reviewed by: two anonymous referees