The Delayed Ionospheric Response to the 27‐day Solar Rotation Period Analyzed With GOLD and IGS TEC Data

The delayed ionospheric response is analyzed for two well‐defined 27‐day solar rotation periods in the year 2019 with solar radio flux index F10.7 and Global‐scale Observations of the Limb and Disk (GOLD) data, like solar extreme ultraviolet (EUV) flux proxy, O/N2 column density ratio and peak electron density, as well as International Global Navigation Satellite System Service rapid high‐rate total electron content (TEC) map data. Although the correlation between GOLD solar EUV flux proxy and TEC is similar to the correlation between F10.7 and TEC, it is shown that the estimated delays based on GOLD data are in much better agreement with recent studies using EUV measurements compared to the delays based on F10.7 data. The GOLD peak electron density correlates well with TEC and allows insight to a local time interval when the ionosphere is not controlled by solar activity changes (17:00 LT to 21:00 LT). The present study investigates the impact of the solar activity (F10.7, GOLD EUV flux proxy) and O/N2 column density ratio on the ionospheric delay for two representative solar rotation periods. The capabilities of GOLD data for future research on the ionospheric response to the 27‐day solar rotation period are demonstrated and discussed. These results are crucial information for precise ionospheric models and forecasts.

studies are difficult due to frequent or big data gaps (Schmölter et al., 2018(Schmölter et al., , 2020. Therefore, the combined analysis of several ionospheric and solar parameters is also important to improve the current understanding of the delay. The recent National Aeronautics and Space Administration (NASA) mission Global-scale Observations of the Limb and Disk (GOLD) provides a set of new data products including a solar EUV flux proxy, the O/ N 2 column density ratio and the peak electron density. This combination of measurements is of interest for the analysis of the ionospheric response time to the 27-day solar rotation period. This study presents first results of such an analysis and compares the findings to solar and ionospheric parameters, that have been commonly used in preceding studies. The potential of GOLD data to characterize the delayed ionospheric response is discussed based on these results.

Data
This study analyses different solar proxies and ionospheric parameters in the time period from January 2019 until December 2019. This period is part of the descending phase of the 24th solar cycle, which is defined by low solar and geomagnetic activity (Pesnell, 2016;Solomon et al., 2010). Two 27-day solar rotation periods from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019 are analyzed in more detail.

Solar Radio Flux Index F10.7
The solar radio flux at a wavelength of 10.7 cm (F10.7) is a well-established solar activity index, which is used in several studies and ionospheric modeling approaches to indicate the solar activity level in general or as a proxy for the solar radiation at wavelengths that are difficult to measure (Tapping, 2013). F10.7 measures the total emission of the solar disk over a period of 1 h centered on the selected epoch (17:00, 20:00, 23:00 UT) and represents the full solar spectrum (Tapping, 2013;Tapping & Charrois, 1994). The ionospheric response to solar activity changes and its delay has been investigated in several studies based on F10.7 (Afraimovich et al., 2008;Jakowski et al, 1991Jakowski et al, , 2002Lee et al., 2012;Min et al., 2009;Oinats et al., 2008;Titheridge, 1973;Zhang & Holt, 2008). F10.7 data are obtained from the NASA/GSFC's OMNI data set through the OMNIWeb interface (NASA, 2020).

Solar and Heliospheric Observatory
The Solar and Heliospheric Observatory (SOHO) Solar EUV Monitor (SEM) measures the solar EUV radiation continuously in two bands from 26 to 34 nm and from 0.1 to 50 nm (Judge et al., 1998;Zanna et al., 2015). This study uses the first order band which contains one of the strongest solar EUV emission lines (He II at 30.4 nm) and which impacts significantly the ionospheric state (Zanna et al., 2015). SEM data are obtained from the University of Southern California (USC) Space Sciences Center (NASA, 2020).

Global-Scale Observations of the Limb and Disk
GOLD measures different features of Earth's thermosphere and ionosphere allowing comprehensive studies of Earth's space environment and the upper atmosphere (Eastes et al., 2020). GOLD is an instrument retrieving measurements based on different scans of the sunlit disk, night disk, and limb (Eastes et al., 2017(Eastes et al., , 2020. The dayside disk measurements are used to derive neutral temperature, O/N 2 column density ratio and solar EUV flux proxy. The peak electron density is derived from the nightside disk measurements and the O 2 density profile is derived from stellar occultation measurements (NASA, 2020). The solar EUV flux proxy, the O/N 2 column density ratio and the peak electron density are of interest for this study on the ionospheric response to solar activity changes.
The satellite is in a geostationary orbit at 47.5°W and measures the full spectrum from 134 to 162 nm (Eastes et al., 2017) producing disk images from ±70° in latitude and longitude (at nadir) as well as limb measurements up to 600 km tangent altitude with different measurements modes (Eastes et al., 2017(Eastes et al., , 2020. The full disk images describing temperature and composition of the thermosphere at approximately 160 km are retrieved by combining scans of the north and south latitudes. Each scan of the full disk (30 min) ends with a limb scan or an occultation if a bright star transits the limb (Eastes et al., 2020). The disk images of the thermospheric temperature at 60 min cadence have a precision of ±55 K and the disk images of the O/N 2 column density ratio at 30 min cadence have a precision of 10%. Both disk images are measured at 250 × 250 km 2 spatial resolution (Eastes et al., 2020). The peak electron density measurements of the equatorial arcs have a latitude resolution of 2° and precision of 10% (Eastes et al., 2020). The O 2 column density measurements at vertical resolution of 10 km have a precision of 10% above 150 km from stellar occultations (Eastes et al., 2020).
The solar EUV flux proxy Q EUV describes the integrated solar irradiance below 45 nm and is derived from the far ultraviolet (FUV) measurements using a look-up-table. The O I 135.6 nm brightness, solar zenith angle and O/N 2 column density ratio are applied in this approach (NASA, 2020) according to algorithms by Strickland et al. (1995), Evans et al. (1995) and Strickland (2004). The sampling rate of Q EUV is approximately 5 s (NASA, 2020).
The O/N 2 column density ratio of the thermospheric species O and N 2 is derived from the dayside measurements. The applied algorithms for this process were developed for data processing with Global Ultraviolet Imager (GUVI) and Special Sensor Ultraviolet Spectrographic Imager, but take advantage of the full spectrum measured by GOLD to reduce the signal-to-noise ratio (NASA, 2020). The approach is implemented according to algorithms by Strickland et al. (1995), Christensen (2003) and Strickland (2004).
GOLD performs scans of the nightside disk each day from 17:00 LT to 21:00 LT (corresponding to 47.5°W) and the peak electron density N Max is directly derived from the O I 135.6 nm night glow emission measurements (NASA, 2020). This algorithm is based on the following assumptions: the ion-ion mutual neutralization is neglected, multiple scattering is neglected, the electron and O + densities are identical and the electron density profile is a Chapman layer profile (NASA, 2020).
The GOLD level 2 data products (solar EUV flux proxy Q EUV , O/N 2 column density ratio and peak electron density N Max ) are provided by NASA through the GOLD Science Data Center (NASA, 2020).

Total Electron Content Maps
The International Global Navigation Satellite System (GNSS) Service (IGS) provides total electron content (TEC) maps of their associate analysis centers (Hernández-Pajares et al., 2009). The maps provide the vertical TEC, which is an integral measurement of the electron density covering the whole ionosphere and plasmasphere. This ionospheric parameter was used by several studies of the delayed ionospheric response to solar activity changes due to the 27-day solar rotation period (Afraimovich et al., 2008;Jacobi et al., 2016;Min et al., 2009;Oinats et al., 2008;Schmölter et al., 2018Schmölter et al., , 2020. Cai et al. (2020a and showed a good correlation between TEC maps and N Max maps. Thus, an investigation of the ionospheric response to solar activity changes based on comparison of IGS TEC maps and GOLD data is justified. The present study uses the rapid high-rate solution (UHR) IGS TEC maps provided by the Universitat Politècnica de Catalunya (UPC). The sampling rate of these maps is 1 h and they are processed by applying a global voxel-defined 2-layer tomographic model solved with Kalman filter and spline interpolation (Hernndez-Pajares et al., 2016;Orús et al., 2005). The UHR TEC maps are provided by NASA through the Crustal Dynamics Data Information System (NASA, 2020).

Comparison of Solar EUV Proxies and Measurements
The time series of F10.7, GOLD Q EUV and SEM solar EUV flux in Figure 1 show differences between all three data sets from January 2019 to December 2019. There is an ongoing decrease of Q EUV and solar EUV flux from April 2019 to July 2019 (approximately 10%) which is superimposed with stronger variations over shorter time periods. From July 2019 onward both data sets have an upward trend but Q EUV increases stronger than the solar EUV flux. The described trend does not occur in the F10.7 data which instead show a constant trend superimposed with stronger variations over shorter time periods. A more detailed representation of the correlation between solar EUV flux and both proxies is shown in Figure 2    This good correlation is due to two well-defined 27-day solar rotation periods occurring in each data set (see Figure 1). The first and second cycle vary approximately similar for the solar EUV flux and Q EUV but are influenced by the ongoing decrease from April 2019 to July 2019. The difference between the first and second cycle is much stronger for F10.7 and a different trend is observed. This explains the lower correlation with the solar EUV flux. Nevertheless, all three time series represent the variations due to the 27-day solar rotation during this period and can be applied for an analysis of the delayed ionospheric response.
At longer time scales the correlation coefficients of F10.7 in Figure 2a decrease less than the correlation coefficients of Q EUV in Figure 2b. This trend continues until F10.7 correlates even better with the solar EUV flux than Q EUV . For example, for the whole year the correlation coefficient of solar EUV flux and F10.7 is 0.70 and the correlation coefficient of solar EUV flux and Q EUV is 0.63.

Comparison of Solar Proxies and TEC
The correlation of solar proxies and TEC is known to vary with several parameters. Local time, geographic or geomagnetic coordinates, seasons and the solar cycle can have different impacts on the ionospheric response (TEC) to solar activity (F10.7, EUV) in each hemisphere (Bergeot et al., 2010;Liu & Chen, 2009). In order to investigate the ionospheric response to the solar activity changes within the 27-day solar rotation period a fixed location (geographic longitude of 0° and latitude of 0°) has been chosen. This allows the comparison of two well-defined 27-day solar rotation periods, which can be observed for maximum TEC from 12:00 LT to 14:00 LT.   Figure 4 confirms that there is no direct correlation of F10.7 and TEC for the whole time period (correlation coefficient of 0.03). The correlation could be improved, for example, by removing seasonal and spatial variations of the TEC values. This is not needed for the further analysis though, since its focus are the discussed 27-day solar rotation periods, which appear in both data sets. Figure 5a shows the selected solar EUV flux proxy Q EUV from January 2019 to December 2019. TEC values in Figure 5b are selected at corresponding times of the Q EUV measurements. The same interpolation as in Figure 3 is applied to retrieve smoothed trends. The difference between F10.7 in Figure 3a and Q EUV in Figure 5a are most significant during the middle of the year. F10.7 has a negligible decrease during this time, but Q EUV has a noticeable decrease of approximately 10% (see also Figure 1). The two periods from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019 also show two significant peaks for each data set in Figure 5. Unlike the trend of F10.7, the peaks of Q EUV are superimposed with an ongoing decrease similar to the trend of TEC. The correlation of Q EUV and TEC is shown in Figure 6 for the whole time period (correlation coefficient of 0.69).
The significant changes of the solar activity from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019 cause corresponding ionospheric variations (see gray areas in Figures 3 and 5). Therefore, these periods are appropriate for the analysis of the delayed ionospheric response. An analysis over longer periods (e.g., the whole year) would require the consideration of seasonal and spatial variations of the ionospheric state (TEC), but such a broad investigation is not aim of this study. SCHMÖLTER ET AL.    Figure 7 shows the peak electron density N Max and TEC in the available time period from March 2019 to December 2019. TEC values have been selected at measurement times of N Max (from 17:00 LT to 21:00 LT). Therefore, a different situation compared to Figures 3 and 5 is presented, since at these times the ionosphere is dominated by recombination and not ionization (Rishbeth & Mendillo, 2001). This explains the lower TEC values in Figure 7  TEC is moderate (correlation coefficient of 0.59) and, thus, similar to the correlation of Q EUV and TEC (see Figure 8). Spline interpolations are not applied to the data in Figure 7, since the deviations are stronger than the expected variations, for example, the 27-day solar rotation period.  Figure 4). An additional trend is calculated for each data set, which removes the linear change of each time series during these periods. The resulting trends in Figure 10 (blue lines) are an acceptable approximation of the 27-day solar rotation period.   (1) and the differences between F10.7, Q EUV and TEC can be ranked according to

Ionospheric Response to the 27-Day Solar Rotation Period
The relative change of the ionosphere (TEC) is much stronger than the change in the solar activity (F10.7 and Q EUV ). The minimum values of F10.7 as well as Q EUV do not show any significant difference between both periods. The TEC values in the second period are smaller than in the first period. This is due to the constant decrease of TEC from March 2019 until July 2019 seen in Figures 3b and 5b.
The peak time t max of each Parameter P can be calculated by simply extracting the time of the maximum according to The calculated peak times can be seen in Figure 10. The different peak times for both 27-day solar rotation periods can be related similar to Equation 2 by defining a delayed ionospheric response to the 27-day solar rotation period, which was investigated in preceding studies with similar observations or modeling results, for example, Ren et al. (2018). The delay τ can be specified using the solar activity proxy S (F10.7 or Q EUV ) and TEC according to The delay between TEC and F10.7 in Figures 10a and 10e (Ren et al., 2018;Schmölter et al., 2018Schmölter et al., , 2020, but similar values have been reported in older publications (Afraimovich et al., 2008;Jakowski et al., 2002;Lee et al., 2012;Min et al., 2009;Oinats et al., 2008;Zhang & Holt, 2008). The calculation process of the delay introduces uncertainties due to the applied basis spline interpolation and smoothing or due to the temporal resolution of the data. These uncertainties have a stronger impact for calculations using F10.7 which is measured at daily resolution. Nevertheless, the results can be used to compare the delayed ionospheric response during both 27-day solar rotation periods.
The delay between TEC and Q EUV in Figures 10c and 10e is 0.08 days and the delay between TEC and Q EUV in Figures 10d and 10f is 1.00 days. These results are much closer to calculated delays in recent studies (Ren et al., 2018;Schmölter et al., 2018Schmölter et al., , 2020. The mentioned influence of uncertainties caused by the interpolation process is less due to the higher sampling rate of Q EUV compared to F10.7. Therefore, a smaller difference to studies based on EUV measurements is expected, for example, Schmölter et al. (2020).
The delayed ionospheric response to the 27-day solar rotation period can also be estimated with cross-correlation analysis (Schmölter et al., 2018(Schmölter et al., , 2020. This method fits the data for the whole time period and the calculated results are expected to be different to the delay estimated based on the peak time of the 27-day solar rotation period. The cross-correlation analysis does not require any filtering of the data and therefore no basis spline interpolation is applied. The cross-correlation for a solar proxy S and the ionospheric state P given by maximum TEC is calculated by The sampling rate of the estimated cross-correlation is defined by the input data set with the lower sampling rate. Therefore, the results based on F1.07 and TEC have a sampling rate of 1 day and the results based on Q EUV and TEC have a sampling rate of 1 h. The delay estimation by cross-correlation analysis benefits from the higher resolution of Q EUV .
The results of the cross-correlation analysis for both solar proxies from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019 are shown in Figure 11. The most significant difference compared to the results in Figure 10 is the cross-correlation based on F10.7 for the second period in Figure 11b. The cross-correlation has no pronounced peak and a reasonable estimation of a delay is not possible in this case. The first period in Figure 11a shows a delay of 0 days. The differences of the results compared to the trends in Figure 10 are most likely due to the lack of smoothing leading to the inclusion of smaller features in this approach. The results of the cross-correlation analysis based on Q EUV have a pronounced peak for both periods and delays of 1 and 13 h are estimated. These delays are also different from the trends in Figure 10 but the increase of the delay during the second period is confirmed. As explained, the comparison of peak times and the cross-correlation analysis describe different delays, but the benefit of higher sampling rates is greater with the cross-correlation analysis.
The results in Figures 10 and 11 confirm previous studies. The solar activity is a driving factor of the delayed ionospheric response (Ren et al., 2018;Schmölter et al., 2020) which is impacted by its change even during a solar minimum with low solar and geomagnetic activity. The O/N 2 column density ratio also influences the response time of the ionosphere to solar activity changes (Ren et al., 2018) and is even more important during the chosen time periods with low solar activity (Rishbeth, 1998). Figure  from 1.06 in the first period to 1.03 in the second period (approximately 3%). This trend could be related to the to the ongoing decrease of the solar activity from March 2019 to July 2019 that is superimposed with the analyzed 27-day solar rotation periods (see Figures 1b and 1c), but other processes could impact the O/ N 2 column density ratio as well, for example, temperature, density, or wind changes caused by atmospheric waves (He et al., 2010).
The O/N 2 column density ratio is known to modulate the ionospheric response time (Ren et al., 2018) and to be impacted by the change of solar activity itself (Luan et al., 2017). The influence of solar activity and O/ N 2 column density ratio is defined according to Equation 8 which describes the photochemical equilibrium in the F region (Rishbeth, 1998).
The electron density n is given by ion production q and loss β. The production is defined by the atomic oxygen concentration [O] and the factor I ∞ that is proportional to the flux of solar ionizing radiation (Rishbeth, 1998). The loss is defined by the molecular oxygen concentration [O 2 ] and the molecular nitrogen concentration [N 2 ] with two corresponding coefficients k (Rishbeth, 1998). The solar activity controls directly the production and the O/N 2 column density ratio controls production as well as loss. An increase of the production caused by a solar activity increase, an O/N 2 column density ratio increase or both relates to a longer ionospheric response time (Ren et al., 2018;Schmölter et al., 2020).
The solar activity and its change is stronger during the period from April 27, 2019 to May 24, 2019 compared to the period from May 23, 2019 to June 19, 2019. A longer response time for the first period is expected according to this difference and the established understanding (considering only the response to the 27-day solar rotation period). The O/N 2 column density ratio is also increased during the first period but the difference is not significant enough to analyze the influence on the delayed ionospheric response. In addition, the processes controlling the O/N 2 column density ratio are complex (He et al., 2010;Luan et al., 2017) and the characterization of their impact would require an extensive analysis that is beyond the scope of this study, for example, a spatial analysis for different regions covered by GOLD measurements.
τ(TEC, F10.7) decreases 0.71 days for the second time period in Figure 10, but the cross-correlation analysis in Figure 6 cannot confirm this. τ(TEC, Q EUV ) increases 0.92 days in Figure 10 and 0.50 days in Figure 11 for the second time period. Considering the good correlation of Q EUV in the chosen time period with actual solar EUV flux measurements (see Figures 1 and 2) and the moderate correlation with TEC (see Figure 9) the delays estimated based on this parameter are expected to be more reliable. Therefore, the change of the delay does not align with expectations which could be due to various processes impacting the ionospheric SCHMÖLTER ET AL. state (e.g., plasma transport due to the equatorial plasma fountain effect) or due to uncertainties in the applied methods. The more complex changes of the O/N 2 column density ratio in Figure 12 could also explain parts of the observed trend, but the estimated delays are not precise enough to perform such an analysis (e.g., due to the sampling rate). The overall O/N 2 column density ratio trend follows the TEC variations though, which is of interest for future studies to analyze the seasonal variations of the delayed ionospheric response in more detail (Schmölter et al., 2020). Especially, the combination of different GOLD data (solar EUV flux proxy Q EUV , O/N 2 column density ratio and eventually O 2 density profile) allows a comprehensive analysis when longer time periods of data are available, for example, by applying superposed epoch analysis.

Conclusion
The analysis of F10.7, Q EUV , N Max , O/N 2 column density and TEC has given a first impression of the capabilities of GOLD data in analyzing the delayed ionospheric response to the 27-day solar rotation period. The following results were obtained in the current study and represent an important starting point for future research in this area: 1. The solar proxies F10.7 and Q EUV show noticeable differences, but are in good agreement for at least two solar rotation periods during the year 2019. The delayed ionospheric response time to the 27-day solar rotation periods from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019 could be retrieved using both data sets (see Figure 10). Q EUV is a more reliable proxy than F10.7, which is not synchronized with the solar EUV radiation at all times (Chen et al., 2011(Chen et al., , 2018. Therefore, Q EUV should be used in data analyses of the ionospheric response to solar activity changes but also for ionospheric modeling approaches 2. Q EUV and corresponding TEC are in good agreement (correlation coefficient of 0.69). The estimated delays based on Q EUV and TEC are similar to the results of studies using actual EUV measurements and TEC, for example, Schmölter et al. (2020) 3. N Max and corresponding TEC are in good agreement (correlation coefficient of 0.59). The daily GOLD measurements of N Max from 17:00 LT to 21:00 LT are of interest to analyze accumulation processes within the delayed ionospheric response 4. The O/N 2 column density ratio provides additional information to the analysis of the delayed ionospheric response considering its importance as shown in preceding studies (Ren et al., 2018;Schmölter et al., 2020). An analysis of longer periods with varying solar activity and O/N 2 column density ratio conditions might allow to estimate their respective impact on the delay 5. It is important to investigate the different ionospheric processes during ionization and recombination periods of the 27-day solar rotation period based on maximum and late noon TEC. GOLD data (Q EUV , N Max and O/N 2 column density ratio) provide critical additional information exactly during these periods 6. Delays τ(TEC, F10.7) of 3.13 and 2.42 days and delays τ(TEC, Q EUV ) of 0.08 and 1.00 days are estimated by comparison of the peak times of the two 27-day solar rotation periods from April 27, 2019 to May 24, 2019 and from May 23, 2019 to June 19, 2019. The results based on Q EUV are qualitatively confirmed with a cross-correlation analysis that estimates respective delays of 0.04 and 0.54 days GOLD data offer the potential to gain more knowledge about the response of the ionosphere to solar activity and to better characterize the occurring delay. The combination of different parameters can contribute to identify their respective impacts on the ionospheric delay. In conclusion, we strongly recommend to include GOLD data in future studies of the delayed ionospheric response to solar EUV radiation.