Ionospheric Response to Solar EUV Radiation Variations: Comparison based on CTIPe Model Simulations and Satellite Measurements

The ionospheric Total Electron Content (TEC) provided by the International GNSS Service (IGS), and the Coupled Thermosphere Ionosphere Plasmasphere Electrodynamics (CTIPe) model simulated TEC have been used to investigate the delayed ionospheric response against solar flux and its trend during the years 2011 to 2013. The analysis of the distinct low and mid-latitudes TEC response over 15◦E shows a better correlation of observed TEC and the solar radio flux index F10.7 in the Southern Hemisphere compared to the Northern Hemisphere. Thus, a significant hemispheric asymmetry is observed. 5 The ionospheric delay estimated using model simulated TEC is in good agreement with the delay estimated for observed TEC against Solar Dynamics Observatory (SDO) EUV Variability Experiment (EVE) measured flux. The average delay for the observed (modeled) TEC is 17(16) h. The average delay calculated for observed and modeled TEC is 1 and 2 h longer in the Southern Hemisphere compared to the Northern Hemisphere. Furthermore, the observed TEC is compared with the modeled TEC simulated using the SOLAR2000 and EUVAC flux 10 models within CTIPe over Northern and Southern Hemispheric grid points. The analysis suggests that TEC simulated using the SOLAR2000 flux model overestimates the observed TEC, which is not the case when using the EUVAC flux model.

equations. SOLAR2000 determine the EUV irradiance for 809 emission lines and also for 39 wavelength bands.

EUVAC solar flux model
Within CTIPe, a reference solar spectrum based on the EUVAC model (Richards et al., 1994) and the Woods and Rottman (2002) model, driven by variations of input F10.7 is used. The EUVAC model is used between 5 nm and 105 nm, and the Woods and Rottman (2002) model for 105 nm to 175 nm. Solar flux is obtained from the reference spectra using the following (1) where f ref and A are the reference spectrum and solar variability factor, respectively, and P = 0.5 × (F 10.7 + F 10.7A), where F10.7A is the average of F10.7 over 81 days.
The EUVAC model includes solar flux in 37 wavelength bins based on the measured F74113 solar EUV reference spectrum 135 (Hinteregger et al., 1981) and the solar cycle variation of the flux.

Comparisons between empirical EUV irradiance variability models and observations
We compare TIMED SEE observations with the two empirical models constructed from direct proxy parameterizations of the EUV irradiance data base, which are used to represent EUV in the CTIPe model. is comparable to the SOLAR2000 flux, with a difference of about 10% and 23% higher than the EUVAC model. The EUVAC flux is about 30% lower than the SOLAR2000 model. The correlation coefficient of EUV from both the EUV flux models with the observed EUV flux is approximately 0.90 during the study period. In summary, the SOLAR2000 model is in relatively good agreement with the observed flux while the EUVAC model underestimates SOLAR2000 and the TIMED SEE flux. These results agree with earlier comparisons (Lean et al., 2003;Woods et al., 2005;Lean et al., 2011, & references therein).
150 Woods et al. (2005) compared the TIMED SEE observations with the flux calculated from different empirical models for 8 February 2002. They reported that the empirical models are within 40% of the SEE measurement at wavelengths above 30 nm.
The EUVAC and SOLAR2000 models agreed best with TIMED SEE, compared to the other models. Lean et al. (2003) validated the NRLEUV model with different empirical models such as SOLAR2000, HSG, and EUVAC.
In absolute scales NRLEUV, HFG and EUVAC have total energies that agree within 15%, but the SOLAR2000 absolute scale 155 is more than 50% higher. Their study reveals that long EUV wavelength (70-105 nm) energy contributions (about 46% of the whole flux from 5 to 105 nm) is the main reason for higher EUV flux in the SOLAR2000 model compared to other empirical models.

Results and discussion
In the following sections, we show the results and discuss the TEC observations and their comparison with the modeled 160 TEC at 15 • E. Furthermore, relations with solar radiation and the delayed response over both the Northern and Southern Hemispheres are presented. Schmölter et al. (2020) has reported on a detailed investigation of the delayed ionospheric response over European and Australian regions. Here, we analyze the delayed response at 15 • E covering the latitudes from 70 • S to 70 • N and compare the response over the South African region with the European region.
In this study we have addressed the following points: 165 1. The TEC variations at moderate solar activity of solar cycle 24 are analyzed to compare the input for the delay analysis.
A characterization of these differences between observed and modeled TEC is important to derive further relations.
2. We used the periodicity estimation (frequency analysis) to study observed and modeled TEC characteristics in detail.
3. The relation between the F10.7 index and hemispheric TEC has been used to analyze the solar and ionospheric inputs of delay estimation. 4. In our study we focus on the ionospheric delay estimation as a main point of our analysis.
5. Observed TEC variations and its comparison with simulated TEC is done by using different flux models. In previous work it has already be shown that the solar activity has the strongest impact on TEC under nominal conditions and is therefore significant for the derived delay.
3.1 TEC variation at moderate solar activity of solar cycle 24

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The ionospheric electron density is strongly varying from day to night depending on the daily variations of solar radiation.  In comparison to observed TEC, the modeled TEC (Figure 2(b)) is lower during the spring and summer period in the Southern Hemisphere, while it is in better agreement during the winter season. The bias between the modeled and observed TEC is higher during the spring and summer season. In general, the modeled TEC is lower than the observed TEC.

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The variations in TEC are not only controlled by the solar radiation, but there are other factors such as local dynamics or geomagnetic activities due to solar wind variations, which also influence the ionospheric state (Abdu, 2016). Fang et al. (2018) studied day to day ionospheric variability and suggested that absolute values in TEC variability at low latitudes are largely controlled by solar activity, while for mid-and high-latitudes, however, solar and geomagnetic activities contribute roughly equally to the absolute TEC variability.

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A detailed comparison between the observed TEC and modeled TEC simulated using the different solar flux models (SO-LAR2000 and EUVAC) during January, June, and December is presented and discussed in Section 3.6.

Periodicity estimation
Solar activity varies at different time scales from minutes to years or even centuries. The periodic behavior in the solar proxies has been studied by various authors to explore the response of the terrestrial atmosphere and especially the T/I region, and to 205 investigate the connection between solar variability and ionospheric parameters (Jacobi et al., 2016;Vaishnav et al., 2019). A widely used method to analyse periodicities in time series is the continuous wavelet transform (CWT). The CWT captures the impulsive events when they occur in the time series (Percival and Walden, 2000;Mallat, 2009). However, the CWT also reveals lower frequency features of the data hidden in the time series. , with a preference for the winter season. These may be connected with planetary wave effects from below (e.g. Altadill et al., 2001Altadill et al., , 2003.

Relation between F10.7 index and hemispheric TEC
240 Solar activity has the strongest effect on ionospheric variations especially during enhanced solar activity. The last solar minimum was extremely extended, and the following solar cycle was quite weak (e.g., Huang et al., 2016), so that meteorological influences become more relevant. To examine the effect of solar activity on TEC variations during a weak solar cycle, we analysed the relationship between F10.7 and mid-day TEC (11:00-13:00 LT). Figure 4 shows

Cross correlation and delay estimation
The possible relations between solar activity, geomagnetic activity, and ionospheric parameters have been studied by several authors (e.g., Abdu, 2016;Fang et al., 2018;Vaishnav et al., 2019). However, in the past studies, due to the unavailability of high-resolution data sets, several studies used only daily resolution. To estimate the ionospheric delay, different ionospheric parameters have been considered using daily resolution data, an ionospheric delay of about 1-2 d against solar proxies has been 265 reported (Jakowski et al., 1991;Jacobi et al., 2016;Vaishnav et al., 2019). Only recently, Schmölter et al. (2020) used SDO EVE and GOES EUV fluxes to calculate the ionospheric delay of about 17 h as a mean value based on hourly time resolution data. This observed delay was also confirmed by numerical physics based models (Ren et al., 2018;Vaishnav et al., 2018).
Here, we investigate the ionospheric delay using hourly resolution observations and compare it with the model simulated TEC. Figure 5 shows the cross-correlation and a corresponding ionospheric delay calculated using SDO EVE observed inte- Figure 5(c) shows the cross-correlation coefficient calculated using the modeled TEC and SDO-EVE flux. The correlation coefficient is higher than the one seen in the observed TEC. In the observed TEC. There are several processes that can influence the behavior of the ionosphere and the real observations such as lower atmospheric forcing or geomagnetic activity. But in the model, lower atmospheric variability is not included except in a statistical sense, which affects the total variability, hence higher 280 correlation is observed in model TEC compared to observed TEC.
The analysis suggests that the model can reproduce similar trends and features, as shown in the observations. The overall correlation coefficient in the Southern Hemisphere is higher than in the Northern Hemisphere. h is observed during August 2012 for mid-latitudes. As an interesting feature can be noted here that the ionospheric delay is increasing with increasing solar activity.

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A similar analysis for the estimation of the ionospheric delay has been performed for the model simulated TEC, as shown in Figure 5(d). The CTIPe model is able to reproduce features seen in the observed TEC ( Figure 5(b)). The ionospheric delay is higher during December and follows the solar activity.
In the higher latitude region (above 60 • latitude in both hemispheres), the ionospheric delay in the model is smaller than in the observations and amounts to about 5-10 h. Simultaneously, the correlation coefficient is high at the high latitude regions 295 in the Southern Hemisphere and is about 0.4, as shown in Figure 5(c). This bias is due to the model limitations such as model input, grid resolution and insufficient physical descriptions (Negrea et al., 2012).
Generally, the ionospheric delay calculated from the modeled TEC is in good agreement with the observed one and it is about 17 h. Furthermore, the ionospheric delay is always higher in the Northern Hemisphere as compared to the Southern Hemisphere. Partly negative correlation has been observed in both the model and the observations. This negative correlation TECU. The modeled TEC using the SOLAR2000 flux model is higher than the one simulated using the EUVAC model. A good 335 agreement between the modeled and observed TEC can be seen at the Southern and Northern hemispheric grid points ( Figure   7(e-f)), where the bias is less than 10 TECU. The analysis for December is shown in Figure 7(c-d). The difference plot ( Figure   7(g-h)) shows a different behavior than in June. The modeled TEC simulated using the SOLAR2000 is in agreement during December over 40 • S, but the modeled TEC simulated using the EUVAC underestimates the observations by about 10 TECU.
Over the grid point 40 • N, 15 • E, both flux models result in an overestimation, and the SOLAR2000 flux model produces