Spatial and seasonal effects on the delayed ionospheric response to solar EUV changes

. This study correlates different ionospheric parameters with the integrated solar EUV radiation to analyze the delayed ionospheric response to test and improve previous studies on the ionospheric delay. Several time series for correlation coefﬁcients and delays are presented to characterize the trend of the delay from January 2011 to December 2013. The impact of the diurnal variations of ionospheric parameters in the analysis at an hourly resolution for ﬁxed locations are discussed and speciﬁed with calculations in different time scales and with comparison to solar and geomagnetic activity. An average delay 5 for TEC of ≈ 18 . 7 hours and for foF2 of ≈ 18 . 6 hours is calculated at four European stations. Through comparison with the Australian region the difference between northern and southern hemisphere is analyzed and a seasonal variation of the delay between northern and southern hemisphere is calculated for TEC with ≈ 5 ± 0 . 7 hours and foF2 with ≈ 8 ± 0 . 8 hours. The latitudinal and longitudinal variability of the delay is analyzed for the European region and a decrease of the delay from ≈ 21 . 5 hours at 30 ◦ N to ≈ 19 . 0 hours at 70 ◦ N has been found. For winter months a roughly constant delay of ≈ 19 . 5 hours is calcu-10 lated. In this study a North-South trend of the ionospheric delay during summer month has been observed with ≈ 0 . 06 hours per degree in latitude. The results based on solar and ionospheric data in hourly resolution and the analysis of the delayed ionospheric response to solar EUV show the seasonal and latitudinal variations. Results also indicate the dependence on the geomagnetic activity as well as on the 11-year solar cycle.

density distribution of the ion species (Kelley, 2009). An understanding of the ionospheric chemical and physical processes is important to provide realistic and reliable physics-based models. The delayed ionospheric response to solar EUV radiation is captured in various ionospheric models (Ren et al., 2018;Vaishnav et al., 2018) and respective simulations can confirm 25 results of previous studies estimating the ionospheric delay with observational data on daily resolution. The calculation of the delay with observational data in high temporal resolution (≤1 hour) is of interest to describe features like seasonal and spatial variations in more detail. The dependence on solar and geomagnetic activity (Ren et al., 2018) can be explored further. In the future, results for the ionospheric delay on high temporal resolution will strengthen the understanding of ionospheric processes and help to validate physics-based models.
(foF2). TEC measures the vertical integrated electron density and can be used to describe changes in the whole ionosphereplasmasphere system due to solar EUV variability. The variations of TEC are mostly controlled by the F2 layer (Lunt et al., 1999;Petrie et al., 2010;Klimenko et al., 2015) and for mid-latitudes the total plasmaspheric contribution to TEC is between approximately 8 to 15 % during daytime and approximately 30 % during nighttime (Yizengaw et al., 2008). The availability of TEC in maps with good data coverage for certain regions (e.g. European or North American region) allows a spatial analysis 50 of the delay and a comparison with the foF2 data for specific locations. On the other hand, foF2 describes only the F2 layer of the ionosphere without complicating contributions from the plasmasphere and lower ionospheric layers. Both ionospheric parameters are highly correlated (Kouris et al., 2004), but variations like different peak time of the diurnal variation (Liu et al., 2014) could have a considerable impact on the delayed ionospheric response. As expected, the results will show that the ionospheric delay is very similar for TEC and foF2.  (Orús et al., 2005;Hernández-Pajares et al., 2016). In preparation for the delay calculation, TEC values at seven ionosonde locations and one region (Europe) were extracted from the IGS TEC maps. For each ionosonde location the nearest grid point in the maps was used.

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The other ionospheric parameter included in the analysis, foF2, is derived from ionosonde station data (NOAA, 2019) provided by the National Oceanic and Atmospheric Administration (NOAA), and are available for the same time periods with temporal resolution of 15 minutes (Wright and Paul, 1981). Figure 1 shows a map of stations used to calculate the ionospheric delay. The geographic and geomagnetic latitudes and longitudes of the stations are shown in Table 2. In the northern hemisphere, the European stations Tromsø, Průhonice, Rome, and Athens were selected (auto scaled), since they 85 cover different latitudes ranging from ≈ 38 • N to ≈ 70 • N. The dense coverage of GPS stations over Europe allows a good comparison with TEC data for these locations (Belehaki et al., 2015). An analysis of the southern hemisphere with the South African region would be preferred because of a similar longitude, but there are some time and data gaps, which prevented a reliable estimation of the delay for the available stations. Instead data from the Australian stations Darwin, Camden, and  Canberra for the analysis in the southern hemisphere are used (auto scaled). These stations cover latitudes between ≈ 12 • S to 90 ≈ 35 • S. The conditions of Earth's magnetic field for the European and Australian stations are comparable with small magnetic declination and similar absolute value of magnetic inclination (see Table 2). The selected stations seem appropriate for a comparison between northern and southern hemisphere due to these similar conditions. The variability of the characteristic ionosphere parameter foF2 measured with ionosondes are compared to the EUV flux. In preparation of the analysis, all data are resampled to an hourly resolution using the mean value and gaps are filled with a linear interpolation. Unlike in Schmölter

Correlation of ionospheric parameters with solar EUV
The delayed ionospheric response to solar variability was calculated by different studies in daily resolution. A selection of 100 these studies are shown in Table 1. A first delay calculation with cross-correlations in hourly resolution was done by Schmölter et al. (2018). Here the previous research is extended by addressing daily and seasonal as well as regional dependencies of the ionospheric delay in high temporal resolution. In the analysis different locations are compared and corresponding time series for ionospheric parameters include different variations: diurnal variations, 27-day solar rotation cycle, seasonal variations.   Figure 2 shows that the correlation on hourly resolution is, as expected, much smaller.
Increases and decreases of the correlation coefficients have the same trend though. A characterization of the correlation trend is possible in all shown resolutions. The varying correlation between solar EUV flux or solar proxies like F10.7 with TEC is known from preceding studies. Solar EUV radiation is not able to describe the ionospheric variability at all time periods and  The trend of the delay with a slight increase over the three years as well as the annual variation are present. The two different approaches have a mean variance of approximately 3.15 hours, which accounts for an uncertainty of approximately 16.04 % in the ionospheric delay calculation. This is an acceptable impact of the diurnal variation on the trend of the delay for characterizing temporal and spatial changes. In earlier studies, the correlation of the ionospheric delay has been calculated for different ionospheric parameters based on daily or hourly resolutions, as shown in Table 1  The results for the European stations are shown in Figure 6 for TEC and foF2. The trend of the correlation coefficients of TEC for the four European stations are very similar. The station Tromsø has more significant peaks (for increases and 170 decreases in the correlation), but follows the same general trend. At the end of each year the correlation decreases significantly  show the largest deviation from the mean of the trends of all stations. Since Tromsø is an auroral station, the processes in the ionosphere for this location are influenced by other mechanisms, e.g., particle precipitation or thermospheric heating controlled by the solar wind (Hunsucker and Hargreaves, 2002). The station is still in the analysis of the delayed ionospheric response as the northern boundary for the European region.
The TEC and foF2 correlation coefficients for the Australian stations are shown in Figure 7. In general, the correlation 180 coefficients of TEC and foF2 are slightly larger than for the European stations. The trend of correlation coefficients for both parameters and the trend for the different stations are in good agreement. The suggested impact of the geomagnetic activity is less present in these results. Most notably, the decrease and minimum in December 2012 does not occur. The difference might be due to further impacts on the correlation, e.g. thermospheric wind conditions or seasonal variations due to composition changes (atomic/molecular ratio), which are not covered in this study, but are known to have a strong impact on the ionospheric 185 state (Rishbeth, 1998;Rishbeth et al., 2000).
The results of the delay calculation through cross-correlations are shown in Figure 8  TEC and foF2 at the Australian stations in Figure 9 is very similar, but shows a less linear increase of the delay in each year.
Contrary to the correlation coefficients in the Figures 6 and 7, the delays show a good correlation with the geomagnetic activity in both hemispheres. Hence, this global trend confirms an additional dependence of the delay on the geomagnetic activity.  Figure 10 shows the data for integrated EUV during the analyzed time period and the calculated delay for TEC at Rome and Canberra. As a very coarse visualization for the correlation between EUV and delay, the linear trends in both data sets are shown as well. The long-term trends of EUV and the delay on the northern and southern hemisphere increase within the chosen time period. Thus, during the solar maximum (cycle 24), long-term changes in the EUV seem to correlate with variations in the delay. A similar behavior was suggested by Schmölter et al. (2018) based on an analysis using 200 GOES data for the same time period. Rich et al. (2003) indicated a smaller delay for solar minimum and a longer delay for solar maximum, and Chen et al. (2015) found a decrease in the trend of the delay with decreasing solar activity. Both analyses calculated the delay at a daily resolution for longer time periods than the one used in this study. The difference between the ionospheric delay for the European and Australian stations in Figures 6 and 7 show only small differences due to the assumed trend with the geomagnetic activity. This trend has to be removed in the further analysis. There- The non-seasonal trends are removed by calculating the difference between the ionospheric delays of both stations. The results are shown in Figure 11. The difference between both stations clearly shows a seasonal variation in the northern and southern hemisphere with a greater delay for Rome in the northern hemisphere summer and a greater delay for Canberra in the 210 southern hemisphere summer. The delay difference varies over different ranges for the parameters: TEC with ≈ 5 ± 0.7 hours Figure 10. Plot (a) shows the the integrated EUV fluxes from 6 to 105 nm and the linear trend of the EUV (dash-dotted line). Plot (b) shows the delays of TEC against EUV for Rome (orange) and Canberra (purple), as well as the linear trends of the delays (dash-dotted lines). and foF2 with ≈ 8 ± 0.8 hours. These results could indicate a stronger seasonal variation of the ionospheric delay in the F2 layer compared to the whole ionosphere-plasmasphere system, but there are other possible sources for the difference (e.g. the background model of the IGS TEC maps). Similar to the discussion of the impact of diurnal variations, such findings need to be confirmed with modeling efforts. In conclusion, the trends of the ionospheric delay for TEC and foF2 are very similar and 215 both ionospheric parameters show features of the seasonal variations.

Analysis of the delay for mid-latitudes
Another trend visible in Figure 8 is a decrease of the delay with latitude in summer. The station at Tromsø shows the shortest delay of the European stations for both parameters. The differences in the delay between Průhonice, Rome, and Athens are smaller. Figure 12 shows the difference between the stations Rome and Tromsø for both ionospheric parameters. The results 220 for TEC show a greater or similar ionospheric delay for the station Rome compared to the station Tromsø. There are only a few short time periods during winter with a greater ionospheric delay for the station Tromsø. A stronger seasonal variation appears for the parameter foF2, but overall the ionospheric delay is still greater for the station Rome. The mean difference for results in Figure 12 is ≈ 1.08 hours for TEC and ≈ 0.52 hours for foF2. The changes with latitudinal dependence of the trends integrated EVE fluxes (6 to 105 nm) for Rome (orange) and Canberra (purple). The temporal resolution is one hour. Equinoxes are marked with the green dashed lines and solstice is marked with the red dashed line. during winter are due to the stronger increase of the ionospheric delay for Rome during summer. No such trend is visible for 225 the Australian stations and there are only minimal differences in the delay. This is probably due to the smaller range of latitudes covered by this stations. A precise interpretation of the trend without data from different latitudes in the southern hemisphere is difficult. Nonetheless, the results for the latitudes over Europe are consistent with the expectations that different and more varying delays can be observed in polar regions due to the direct impact of the solar wind (Watson et al., 2016) as well as for the equatorial region due to the strong dynamics in ionosphere and thermosphere (Maruyama, 2003).

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A further analysis of the mid-latitude delay is possible using TEC data over Europe, where a good observational coverage from GNSS stations and only minimal influence by the ionospheric model is expected. Therefore, the region from the TEC maps (30 • N to 70 • N and 10 • W to 30 • E) can be extracted and the time series of the delay for each available grid point can integrated EVE fluxes (6 to 105 nm) for Rome (orange) and Tromsø (black). The temporal resolution is one hour. Equinoxes are marked with the green dashed lines and solstice is marked with the red dashed line. be calculated. This was done by cross-correlations with a time window of 90 days and a step length of one hour in Figure 13, which maps the mean delay values for the mid-latitudes in summer (May-August) and winter (November-February). Figure   235 13 shows ionospheric delays that are consistent with the results from the European ionosonde stations in Figure 8. In winter, there is no strong increase or decrease with latitude, but roughly the same delay of ≈ 19.5 hours over the entire region. The decrease of the ionospheric delay at latitudes greater than 65 • N and smaller 35 • N confirms a latitudinal trend, which was found in preceding studies (Lee et al., 2012). A similar behavior of the delay has been found by Ren et al. (2018). In summer, the delay decreases with increasing latitude. From ≈ 21.5 hours at 30 • N to ≈ 19.0 hours at 70 • N, or ≈ −0.06 hours per degree 240 in latitude. Therefore, the delay maps confirm the latitudinal variations as seen in Figures 8 and 12. The variation in delay with longitude is small and does not show any dominant trend in winter. The variation of the delay with longitude in summer is much smaller than the variation in latitude for the same season, with a change of ≈ −0.01 hours per degree in longitude.
The small and similar magnetic declination for the European region could be related to the small variations of the ionospheric delay with longitude. There is an influence of the magnetic declination on the mid-latitude ionosphere, which leads to similar 245 longitudinal transport processes in all seasons (Zhang et al., 2012(Zhang et al., , 2013. This behavior has to be explored with observational data for different regions or modeling efforts in the future. For the further analysis the calculated time series of delay maps is averaged over longitude to get a mean value for the delay at each latitude. The results are summarized with epoch plots in Figure 14 having a resolution of one week (mean value) to allow a better presentation of the long-term changes of the ionospheric delay. The latitude-dependent time series in Figure 14 is 250 consistent with the results and the assumed trend from the seasonal variations is present. In October, the delay reaches the same value for all latitudes and does not change any more until the sudden decrease in December, which happens for all latitudes.
The trend based on the geomagnetic activity (see Figures 4 and 5) is also represented in Figure 14. -The analysis of IGS TEC maps covering the European region indicates a latitudinal dependence of the delay for midlatitudes, which is pronounced in summer and vanishes in winter. A North-South trend of the ionospheric delay during summer month has been observed with ≈ 0.06 hours per degree in latitude.
For the seasonal variation the difference in the delay was calculated at stations of similar latitude in both hemispheres for TEC with ≈ 5±0.7 hours and foF2 with ≈ 8±0.8 hours. The decrease of the delay with latitude in the European mid-latitudes from 275 ≈ 21.5 hours at 30 • N to ≈ 19 hours at 70 • N in summer and the roughly constant delay of ≈ 19.5 hours for the whole region in winter also show a seasonal difference in the delay.
Future analysis would benefit from high resolution ionospheric delay calculations for longer time periods that cover different solar and geomagnetic activity conditions. This requires better and more EUV measurements though. The thermospheric conditions (e.g. neutral winds or composition changes in the atomic/molecular ratio), which are known for their impact on the 280 ionosphere (Rishbeth, 1998;Rishbeth et al., 2000) should be included in future analysis as well. Results presented need to be further confirmed and studied by model calculations. The underlying processes for the delayed ionospheric response to solar EUV radiation need to be described, since this knowledge is an opportunity to validate or improve physics-based models.