A New Index to Describe the Relationship between Solar Extreme Ultraviolet Variation and Solar Activity

In this paper, a new solar activity index based on a novel disturbance extraction method, the spectral whitening method (SWM), is introduced to process the solar EUV data on the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. Our research suggests that the spatial information derived by SWM can well reflect the location of disturbance extraction, which is consistent with the location of the solar active region. It indicates that the disturbance extraction is effective. From AIA 094 Å to AIA 335 Å, SWM results are strongly correlated with solar radio flux F107 and the sunspot number (SSN), especially at AIA 211 Å, where the correlation coefficient reaches the maximum, while at AIA 1600 Å and AIA 1700 Å there are no detectable correlations. The proposed new solar activity index, JPAIA , has the following characteristics: (1) the new index can reflect the main variations of F107 and SSN, indicating that the index is valid; (2) the new index has higher temporal resolution, which is more conducive to the more detailed study of solar activities on short timescales; (3) the new index reveals that the solar atmosphere still has significant variability during solar minimum characterized by low F107 and SSN; (4) the new index can be used in conjunction with the new magnetospheric and ionospheric indices, which are also derived by SWM to deepen the understanding of the causal chain of space weather and promote the improvement of forecasting capabilities.


Introduction
The solar extreme ultraviolet (EUV) irradiance is a major source of heating and ionization in the Earth's upper atmosphere.It dominates the formation of the ionosphere and can significantly modify the upper atmosphere, and drives many major processes in solar-terrestrial space.Thus the reliable specification of solar EUV variations as the input of many space weather methods and models will be critical to improve the space weather prediction skill and research level.Models such as SAMI (Huba et al. 2000), TIMEGCM (Solomon & Qian 2005), GITM (Ridley et al. 2006), the Global Average Mass Density Model (Emmert et al. 2008), and the Global Assimilative Ionospheric Model (Schunk et al. 2004) all require solar EUV irradiance as input.
Early solar index research was dominated by ground-based observations, with the solar index F107 (derived from the solar 10.7 cm radio flux) regularly monitored by ground-based observatories (Tapping & Zwaan 2001), and the value of F107 is determined daily.The 10.7 cm radio emission originates from the chromosphere and low corona of the Sun, and F107 has been widely used in the field of ionospheric and atmospheric research as a representative of the solar EUV radiation and hence the solar activity.The index has been reliably and routinely measured on the ground for up to 70 yr.Unlike many other solar parameters for index construction, the solar 10.7 cm flux can easily be measured reliably on a day-today basis from the Earth's surface, in all types of weather.The previous mentioned models prefer the F107 as the proxy of the solar activity; however, the F107 is limited by the long measurement interval and cannot timely reflect the impact of solar activities on the Earth's atmosphere.The explanation to the apparent connection between F107 and the geospace phenomena has to go back to the EUV (or even shorter) emissions from the Sun.
With the development of solar space-based observations, the SOHO (Solar and Heliospheric Observatory) launched jointly by ESA and NASA has further improved the understanding of the Sun.This was followed by the advent of the solar index Mg II (Heath & Schlesinger 1986), which further improved the characterization of solar EUV, and direct and indirect comparative studies of Mg II and F107 with measured EUV radiation showed that Mg II was better than F107 in most cases, especially that of the He II 30.4 nm line (Lean et al. 2001;Viereck et al. 2001;Lean et al. 2003).When Mg II and F107 are used as input for short-term forecasting of thermosphere, the results show that Mg II is also better than F107 (Guo et al. 2007).In order to fully understand the energy output of solar radiation, Snow et al. (2005) used the Solar Stellar Radiation Comparison Experiment Device on board SORCE to modify the Mg II index to further improve its ability to describe the solar EUV.It can be seen that the development of solar EUV index is inseparable from the progress of solar observation technology.
Recently, the successful launch of the FengYun-3E satellite on 2021 July 5 marks an important progress in China's space-based solar observation; the satellite is equipped with the first Chinese solar EUV imaging instrument, which has autonomous tracking and image stabilization functions to track the Sun in real time and avoids image blur that is caused by other disturbances, and its time resolution is as high as 7 s (Chen et al. 2022;Yang et al. 2023).It is very suitable for the development of a high-temporal-resolution solar EUV index.
Since more and more solar EUV observations are available, researchers are trying to construct new solar activity indices from various of EUV observation so as to get more understandable results.At the verification stage, the applicability of the new indices usually verified by check their consistence with the sunspot number (SSN) or F107.However, SSN typically have one value per day, and the F107 index currently used is similar; neither F107 nor SSN can satisfy the requirements of the high-precision prediction model.In particular, the recent popular prediction models based on deep learning algorithms, whose performance has been proved by many works, have to face the big problem in that the accuracy of their models cannot exceed the time resolution of the data themselves (Chen et al. 2019;Tang et al. 2021aTang et al. , 2021b;;Chen et al. 2022;Wang et al. 2022).Therefore, new solar activity index with higher resolution is urgently needed.In this present paper, the Atmospheric Imaging Assembly (AIA) EUV data are used to construct a new EUV index by the spectral whitening method (SWM), which can effectively remove background variations from time series data and extract aperiodic disturbance information (Chen et al. 2014;Wang et al. 2014;Chen et al. 2017aChen et al. , 2017b;;Zhao et al. 2018;Li et al. 2020aLi et al. , 2020b;;Zhao et al. 2022).The performance of the new index is validated by the investigation on the effects of EUV radiation at different wavelengths on geomagnetic activity.
In this present paper, first the data format, the sources, and the specific processing of data by SWM are introduced.Then we construct and compare the new index, ( ) J AIA P , with F107 and SSN, and analyze the performance of ( ) J AIA P during some solar bursts.At last, the necessity and significance of the new index are discussed.

Data and Method
The EUV data used in this paper are from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012), which provides images, i.e., the global coronal image (GCI), of the full-disk corona at EUV wave bands.the AIA (Lemen et al. 2012) on board SDO persistently captures the full-disk corona at a cadence of 12 s and records coronal images with nine EUV channels.The AIA data during 2021 January 1 to 2021 December 31 are adopted for this research from http://jsoc.stanford.edu/ajax/lookdata.html,with a time resolution of 12 s to 1 hr.The image resolution is 4096 * 4096, and the wavelengths are 94, 131, 171, 193, 211, 304, 335, 1600, and 1700 Å.It should be noted that the seven bands from 94 to 335 Å mainly represent the upper solar atmosphere while 1600 and 1700 Å mainly represent the lower solar atmosphere, and hence the variations at 1600 and 1700 Å bands usually are not consistent with those at the other seven bands (Lemen et al. 2012).AIA provides an unprecedented combination of spatial resolution, field of view, wave bands, and temporal coverage for coronal imaging.Therefore, the huge amount of AIA EUV data will be a reasonable observation for constructing a new solar activity index with high temporal resolution.
The SWM was proposed to identify aperiodic ionospheric disturbances by Wang et al. (2014) and proved to be effective in extracting disturbances in the ionosphere and geomagnetic field (Chen et al. 2014(Chen et al. , 2017a;;Zhao et al. 2022).To facilitate data processing, each AIA image is reduced to the pixel matrix of 100 * 100 by the bicubic interpolation function of OpenCV, to construct an AIA image matrix of 61368 * 100 * 100.We extract every matrix elements to form 10,000 time series.And then the SWM is applied to these time series.At last, we calculate the average value of the SWM result at the same time.For a time series ( ) g t i , the algorithm of the SWM to calculate deviation is as follows: where the ( ) * t g id and x ( ) p env represent the SWM result of each grid and the upper envelope of the power spectrum of ( ) t g i , respectively.The p 0 is the mode in the data set of x ( ) p env . ( )t g m is the weighted average of ( ) * t g id .In this paper, the GCI grid represents the pixel matrix of each AIA image converted to 100 * 100, and the element of the matrix corresponds to each grid of the GCI.That is, each GCI grid is denoted as an element of ( ) g t i .An improvement on the basis of Wang et al. (2014) and follow-ons, a Savitzky-Golay filter is applied to ( ) t g m to denoise the signal by fitting successive subsets of adjacent scattered data points with a lowdegree polynomial through the use of linear least squares, while increasing the signal-to-noise ratio of a corrupted signal without distorting it very much (Selver et al. 2018).This improvement ensures the shape and width of the signal are unchanged while filtering out the noise.For a single wavelength, we take the result of ( ) t g m passing through the Savitzky-Golay filter as the new defined disturbance index.The disturbance index at a single EUV channel is calculated as follows: where σ is the standard deviation of ( ) t g m , and the subscribe S refers to "single wavelength." Figure 1 shows the J s in the year 2021 at different AIA bands, or denoted as J s (AIA).As mentioned above, the radiations at 1600 and 1700 Å originate from a different sphere from that of other wavelengths.So it is not surprising that J s (1600-1700 Å) shows a different trend from J s (094-335 Å).
We define a new solar activity index ( ) J AIA P to describe the general variation at all bands based on the average of J s (094-335 Å): where AIA in parentheses indicates that this index is constructed from AIA images since the same indices can also be derived from other solar parameters.

Results and Analysis
To investigate the capability of the new indices to describe the solar activity, the comparison between ( ) J AIA can present most characteristics of F107 or SSN.In fact, each J s at AIA EUV bands (except for 1600 and 1700 Å) is also highly correlated to F107 or SSN, while J s (211 Å) shows the maximum correlation coefficient, approaching 0.88.This result shows that the SWM can effectively extract the variations in the solar EUV radiations, as has happened in ionosphere and geomagnetic field research (Wang et al. 2014;Chen et al. 2017aChen et al. , 2017b;;Zhao et al. 2022).Thus, the index J s is suitable for describing the solar activity at the corresponding EUV band, and ( ) J AIA lP could be used as a new proxy of the solar activity at least as well as F107 or SSN.As expected, J s (1600 Å) and J s (1700 Å) are not correlated with F107 and SSN.This is an interesting phenomenon; according to the instrument characteristics of SDO/AIA (Lemen et al. 2012), the observational data of AIA 1700 and 1600 Å channels mainly correspond to the temperature minimum, photosphere, upper photosphere, and transition region in the lower solar atmosphere with lower temperatures, while 211, 193, 131 Å, and other AIA channels mainly correspond to high-temperature components in the upper solar atmosphere.For the same solar activity, observational images of these two channels, 1600 and 1700 Å, have different characteristics from other AIA channels.Lemen et al. (2012) showed that sunspots appear as dimming areas darker than the surrounding area in the 1600 and 1700 Å channels, while they show very pronounced bright areas in the high-temperature AIA channels such as 211, 193, and 131 Å.However, for the plage and flare, all of these channels in turn appear as brightened areas.In addition, solar activity causes variations in all wavelengths of solar radiation, with larger  changes at shorter wavelengths (Fröhlich & Lean 2004).For example, flares can bring several orders of magnitude of enhancement in the solar soft X-ray flux, but there may be only a small change in the white light images.Therefore, the two low-temperature channels, 1600 and 1700 Å, should not be completely consistent with the high-temperature channels of AIA.
Based on the reasons above, the 1600 and 1700 Å observations will not be considered in further discussions.And this difference also suggests that in research one should not treat AIA 1600 Å and AIA 1700 Å as the same as other wavelengths.
As mentioned previously, a meaningful index trying to describe the solar activity should be verified by F107 or SSN.The comparison of J s (094-335 Å) with F107 as well as SSN is shown in Figure 3. From 94 to 335 Å, all the J s indices show a gradually increasing trend in 2021 that reaches its peak in December, which agrees with the trend of either F107 or SSN.Among them, J s (171 Å) changed sharply during the solar eruption event in October and 2021 November.Since each J s (094-335 Å) behaves consistently, it is not surprising to see that the ( ) J AIA P has a high correlation with F107 and SSN (Figures 2 and 4).
The solar eruption event in 2021 October and November is used to check the applicability of the J s index during solar burst.During this event, the overall intensity of AIA images increased significantly at all wavelengths.Herein we take 171 and 193 Å as the example (the first and third panel in Figure 5) and calculate J s (171 Å) and J s (193 Å) (the second and fourth panel in Figure 5) to carry out the investigation.As shown in the Figure 5, both J s (171 Å) and J s (193 Å) successfully sketch out the areas with high EUV radiation intensity in the solar disk, including the solar flare bursting on October 30.It can be seen that during this period the main active areas are located in the midlatitude regions, and it is revealed by J s more clearly (as clarified by the green horizon dashes in the second and fourth panels in Figure 5) than by the original radiation intensity.
Moreover, ( ) J AIA P also presents some merits that F107 and SSN lack.At first, ( ) J AIA P has a temporal resolution of 1 hr because of the average window to the AIA observations chosen as 1 hr in this paper due to the computation amount (while one should keep in mind that the AIA observation resolution is 12 s, which leaves a big space to improve the temporal resolution of ( ) J AIA P in the future).On the other hand, both F107 and SSN are given at a resolution of 1 day and it makes F107 and SSN inconvenient or even impossible to be adopted for investigating events with durations of only several days or even less than 1 day.Second, as shown in Figure 3, there are many periods (e.g., during the spring in 2021) that SSN keeps as 0 while F107 is at normal level, while ( ) J AIA P is negative to hint that the solar activity is lower than an average level.SSN = 0 is a natural defect of the sunspot number, since there being no sunspot absolutely does not mean the Sun is not active.To clarify the two differences among ( ) J AIA P with F107 and SSN, solar activity that occurred in 2021 January is investigated (Figure 6).During this period, SSN is 0, and F107 is below 80.Moreover, the limitation of their time resolution (only one value per day) has the result that no time variation can be found within 1 day.For ( ) J AIA P , it is possible to find many shorter-timescale variations.And the negative value of ( ) J AIA P can be found during the low solar activity day, which hints that the solar activity is even lower than what the low SSN and F107 indicate.

Discussion and Conclusion
The F10.7 index represents radio emissions originating in the chromosphere and the corona of the solar atmosphere.And SSN is an index of the sunspot number that shows the activity of solar active regions.They are good solar activity indices; however, physically speaking, they cannot fully accurately describe the EUV changes of the Sun, which is essential for  In the solar minimum, when the SSN is close to 0 and F107 is low and stable, there are still solar activities such as coronal holes and filaments in the solar atmosphere, so EUV radiation still has significant changes, but SSN and F107 cannot effectively reflect these changes.For example, EUV may decline when coronal holes are more pronounced, and the solar atmosphere is still active.Previous indices had difficulty describing this situation, but Js and Jp have this ability to describe it.Especially in the case of negative values, corresponding to the change of the coronal structure of the Sun, the highly dynamic characteristics of the corona can be well reflected in the EUV radiation, which is an important supplement and improvement to the SSN and F107 indices focusing on the lower solar atmosphere.The new index not only has the ability to describe solar activity with high temporal resolution, but also reveals some phenomena that cannot be described by other indices, which is conducive to the study and prediction of solar activities at different temporal and spatial scales such as solar flares and coronal holes.
All in all, the SWM is a promising approach for constructing new solar activity indices.This method involves a mathematical algorithm that can remove unwanted periodic spectral features from the data, resulting in a more accurate representation of the disturbance of EUV radiation emitted by the Sun.Through present analysis, it suggests that the AIA data during this period can reflect the effectiveness of the SWM index.From the above results, the main conclusions are presented as follows: 1.The SWM can effectively extract the disturbed variation from solar EUV observations, just as it has done in research related to the ionospheric and geomagnetic field (Chen et al. 2014;Wang et al. 2014;Chen et al. 2017aChen et al. , 2017b;;Zhao et al. 2018;Li et al. 2020aLi et al. , 2020b;;Zhao et al. 2022).This suggests that SWM can be considered a unified method to be used to explore the disturbance chain from the solar activity to the behavior of Earth's magnetosphere, and then to that of the ionosphere in the future.2. Using SWM and new EUV data, a new solar activity index can be obtained and have the following features: (1) the new index can reflect the main variation features of F107 and SSN, indicating that the index is valid; (2) the new index has higher temporal resolution, which is more conducive to the more detailed study of solar activities on short timescales; (3) the new index reveals that the solar atmosphere still has significant variability during solar minimum characterized by low F107 and SSN; (4) the new index can be used in conjunction with the new magnetospheric and ionospheric indices to deepen the understanding of the causal chain of space weather and promote the improvement of forecasting capabilities.
well as SSN in 2021 is shown in Figure 2. It can be seen that ( ) J AIA lP has very similar variations to those of F107 and SSN.The correlation coefficient between ( ) J AIA lP and F107(SSN) is up to 0.88 (0.81) in the whole year of 2021, indicating that ( ) J AIA lP

Figure 1 .
Figure 1.The result of modified SWM (with a Savitzky-Golay filter) for nine AIA EUV channels.

Figure 2 .
Figure2.The correlations between ( ) J AIA P (J s ) and F107 (SSN).The results showed that the SWM changes at different wavelengths from from 094 to 335 Å showed high correlation with F107 (SSN), but 1600 and 1700 Å shows no correlation.

Figure 3 .
Figure 3.Comparison among J s (094-335 Å).It reads that the SWM derived variations at different wavelengths from 094 to 335 Å show a generally similar trend.

Figure 5 .
Figure 5.The AIA EUV images at 171 and 193 Å (panels 1 and 3 from top), as well as the derived J s indices (panels 2 and 4) around a coronal mass ejection event.

Figure 6 .
Figure 6.A case analysis on the time variation of ( ) J AIA P and F107, when the solar index R remains at zero during the period of 2021 January.The images (top two panels) are the AIA EUV images at AIA 193 Å.