Temporal Variability of Equatorial Ionization Anomaly Crest Locations Extracted From Global Ionospheric Maps

The Equatorial Ionization Anomaly (EIA) crest location is known to vary over a variety of temporal scales. For the first time we perform a statistical survey of the temporal variation of the EIA crest location viewed globally and spanning 20 years. We extract the crest location for double‐peaked EIAs from a data set of total electron content intensifications identified on global ionospheric maps from 2003 to 2022. We show that the dominant temporal variations of the crest latitude are annual and semi‐diurnal for the northern crest, and annual and diurnal for the southern crest. For the annual variation, we find that both crests move poleward in local summer and equatorward in local winter, which is more pronounced for the southern crest than the northern crest, and more pronounced at solar minimum than solar maximum. For the diurnal and semi‐diurnal variations in universal time, both crests dip southward around 15UT and the northern crest additionally dips southward around 2.5UT. We consider apparent universal time dependence to be a proxy for the longitudinal distribution of the crest geomagnetic latitude, which exhibits the known wave‐number‐four longitudinal structure of EIA crests. In local time, the EIA crests form earlier than 10LT and move poleward to their maximum distance at 14LT, and remain at constant latitude until 18LT. Solar cycle modulation on the diurnal/semi‐diurnal variations and the local time evolution of the crest latitude is minimal.


Introduction
The most prominent feature of the low-latitude ionosphere is the Equatorial Ionization Anomaly (EIA), which is characterized by accumulations of plasma, or "crests", near ±15°in geomagnetic latitude, with a trough at the geomagnetic equator (Appleton, 1946(Appleton, , 1954;;Namba & Maeda, 1939).The EIA is driven by the combined effects of upward E × B drift, diffusion, and neutral winds (e.g., Balan et al., 2018), through a mechanism known as the equatorial plasma fountain, which siphons plasma from the geomagnetic equator to the EIA crest latitudes.The EIA is most often observed by in-situ and remote-sensing ionospheric electron density or total electron content (TEC) measurements along a certain longitude or local time range as latitudinally double-peaked electron density/ TEC structure.The morphology of the double-peaked structure is known to be variable longitudinally and temporally, in response to external driving such as solar irradiance, geomagnetic activity, lunar phase, and forcing from the lower atmosphere (e.g., Walker, 1981; Y. N. Huang & Cheng, 1996;Yeh et al., 2001;Mannucci et al., 2005;Sagawa et al., 2005;Immel et al., 2006;Mendillo, 2006; J. Y. Liu et al., 2013;Luan et al., 2015;Eastes et al., 2019;J. Liu et al., 2020;T.-Y. Wu et al., 2020;Cai et al., 2023).While single-peak, three-peak, and even four-peak latitudinal EIA structures have been observed as well (e.g., L. Huang et al., 2014;Fathy & Ghamry, 2017;Astafyeva et al., 2016;Maruyama et al., 2016;Xiong et al., 2019), the present study focuses on the classical double-peaked EIA structure, in particular the latitudinal locations of the crests.
The latitudinal locations of EIA crests have been addressed by numerous studies.The crests' latitudinal locations are found to exhibit not only longitudinal dependency but also temporal variability at several scales such as diurnal, seasonal, and solar cycle scales.For instance, the EIA crest latitude and magnitude at a constant local time show a wave-number-four longitudinal structure, which has been attributed to lower atmospheric tides modulating the equatorial plasma fountain via the zonal electric field (England et al., 2006;Immel et al., 2006;Nigussie et al., 2022;Sagawa et al., 2005).The wave-number-four longitudinal structure starts to develop in local morning, becomes most prominent between local noon and early afternoon, and subsides before midnight (Lin, Hsiao, et al., 2007).Yeh et al. (2001) examined the northern EIA crest in TEC data along 121°E during October and November 1994 and found it to form near the equator in local morning, move poleward, and stay at its highest latitude for several hours before receding equatorward, mirroring the diurnal variation of the equatorial electrojet (EEJ).Lin, Liu, et al. (2007) looked at the diurnal motion of EIA crests using three-dimensional images of electron density from FORMOSAT-3/COSMIC satellites during July -August 2006 and revealed that there is asymmetry in the northern and southern EIA crests' latitudinal movement.Chen et al. (2016) analyzed the EIA in the topside ionosphere with ion density measurements from ROCSAT-1 and DMSP satellites during 1999-2004.They found that the double-peaked EIA structure at 600 km altitude appears later than the structure at the ionospheric F2 layer in a day, and it has seasonallydependent longitudinal variations.The seasonally-dependent longitudinal variations of the geomagnetic latitudes of EIA crests have also been identified in Global-scale Observations of the Limb and Disk (GOLD) observations and attributed to the varying distance between the geomagnetic equator and the subsolar point by Eastes et al. (2023).
Annual and semi-annual variations of the crests' latitudes, along with their solar cycle dependency, have been investigated extensively.The annual variation has often been reported to move the winter crest equatorward and the summer crest poleward, which could be caused by the meridional neutral wind and/or the subsolar point location (Tsai et al., 2001;Khadka et al., 2018;J. Liu et al., 2020;Mo & Zhang, 2021).The semi-annual variation refers to the more poleward crest around equinoxes and more equatorward crest around solstices, which has been explained by the meridional neutral wind and/or semi-annual variations in the equatorial electric field strength due to direct solar heating over the equator at equinoxes (C.-C.Wu et al., 2008;Zhao et al., 2009;Mo et al., 2018;J. Liu et al., 2020;Mo & Zhang, 2021).Both the annual and semi-annual variations appear to be stronger during solar minimum than during solar maximum (L.Huang et al., 2013;J. Liu et al., 2020).Moreover, the annual/semi-annual variations can be more distinct in certain longitudinal sectors than others (J.Liu et al., 2020).In addition, while Y. N. Huang and Cheng (1996) reported no significant solar cycle effect on the EIA crest latitude in a limited geographic region in Asia using TEC data from 1985 to 1994, linear relationships have been established between crest latitudes and F10.7 index from global radio occultation measurements during 2003-2014 (Li et al., 2017), as well as radio occultation and in-situ ion density measurements covering the globe during 2013-2019 (Nigussie et al., 2022): both northern and southern crests moved poleward with a higher F10.7.
The above-mentioned studies have contributed significant knowledge to the variability of the latitudinal locations of EIA crests.However, most of the studies are limited by either the geographic region or local time coverage of the measurements analyzed.In this work, we utilize global ionospheric TEC maps that provide global and timecontinuous data coverage over decades to analyze the latitudinal locations of EIA crests.Specifically, our approach is based on a 20-year TEC intensification data set obtained from global ionospheric maps (GIMs).Thus, we are able to consider the EIA as a two-dimensional object with possible longitudinal extent, on a global scale.This simultaneous consideration of longitudinal, latitudinal, and temporal dimensions can only be achieved with time-dependent longitudinal-latitudinal maps of ionospheric electron density or relevant physical parameters that cover either the entire globe or a significant portion of the globe, for example, global TEC maps and GOLD OI 135.6 nm emission maps (Eastes et al., 2019).Our result offers the first statistical characterization of the crest locations viewed globally.We extract double-peaked EIA structures from the data set and investigate major periodic modes in the latitudinal variation of the EIA crests.The annual, diurnal, and semi-diurnal variations of the crests' geomagnetic latitudes, as well as the solar cycle dependency of these variations are examined in detail.We present our data set and approach in Section 2. The statistical properties and major periodic modes of the crest locations are reported in Section 3. Section 4 provides interpretation of the main results, and Section 5 concludes the paper.

TEC Intensification Data Set
The study utilizes a 20-year data set of TEC intensifications, which refer to areas of elevated TEC compared to surrounding areas on TEC maps.The data set contains characteristics of TEC intensification regions with spatial scales greater than 800 km for every 15 min from year 2003 to year 2022 (https://doi.org/10.48577/jpl.KXY5BW).The data set was generated from the JPLD GIM data product by Jet Propulsion Laboratory (JPL), which provides global TEC maps with 1°by 1°spatial resolution and 15-min temporal resolution from year 2003 to present (https://sideshow.jpl.nasa.gov/pub/iono_daily/gim_for_research/jpld/).The production of these global TEC maps is based on interpolating Global Navigation Satellite System (GNSS) TEC measurements obtained from worldwide ground-based receivers (Iijima et al., 1999;Mannucci et al., 1998) (Figure S1 in Supporting Information S1).The JPLD GIM data has been thoroughly validated against independent ionospheric TEC data over land and ocean, and excellent agreements have been found, especially for the low-latitude region where EIA appears.Although the GIM as an interpolated data product provides less accuracy than in-situ ionospheric measurements in local regions with few GNSS receivers, it offers reliable TEC data with full global and local time coverage for investigating large-scale TEC structures and their spatiotemporal variations.
Feature extraction software was applied to identify the TEC intensifications from the JPLD GIM.The software utilizes image processing methods from OpenCV (Itseez, 2015) to extract regions with enhanced TEC on global TEC maps, with adjustable input parameters to define the boundaries of the intensifications and constrain the spatial scales of the intensifications if desired.The workflow of the feature extraction procedure contains several major steps including computing Laplacian values, applying dilation and erosion, merging and removing objects (Figure S2 in Supporting Information S1).The development, implementation, and application of the feature extraction software are described in detail in Verkhoglyadova et al. (2021); Verkhoglyadova et al. (2022); Meng et al. (2024).Applying the feature extraction software to each JPLD global TEC map during 2003-2022, we have obtained the TEC intensification data set, which records the number of intensifications per TEC map and several characteristics of each intensification (Meng & Verkhoglyadova, 2023).The intensification characteristics include the maximum, median, and minimum TEC within an intensification region, the geographic longitude and latitude of the TEC maximum, regional electron content as an indication of the intensification strength, intensification size, and the number of GNSS receivers located within and nearby the intensification region.For a more complete description of the data set and how it was generated, we refer the readers to Meng et al. (2024).

Extracting EIA Crest Locations
The double-peaked EIA structure contains two TEC enhancement regions northward and southward of the geomagnetic equator.These two TEC enhancement regions are identified as two separate intensifications by the feature extraction software and included as part of the TEC intensification data set.As the data set includes characteristics of the TEC intensifications, EIA crest locations can be extracted from the data set.
First, to focus on double-peaked EIAs, we obtain all two-intensification cases from the TEC intensification data set.The data set consists of 43.7% two-intensification cases, which correspond to 306,414 global TEC maps identified with two intensifications from 2003 to 2022.Second, we require that the locations of the maximum TEC within the two intensifications to be separated by less than 45°in longitude, that is, three local hours.This criterion further removes cases when the two intensifications are longitudinally distant.60.5% of the twointensification cases meet the criterion, which gives 185,326 two-intensification cases that are considered as TEC enhancement regions of EIAs.These two-intensification cases are our final selections.86% of the selected intensifications are in close proximity to one or more GNSS ground receivers, indicating reliable TEC data for those intensifications (Figure S3 in Supporting Information S1).Finally, for each two-intensification case selected, we define the maximum TEC within each of the two intensification regions as the EIA crest and extract the geographic latitude and longitude of this local TEC maximum, that is, the EIA crest, from the data set.We also define the EIA northern crest as whichever crest located further north, and designate the remaining crest the EIA southern crest.Our definition of the EIA crests is different from the typical definition of crests in a double-peaked EIA structure, often retrieved via observations along a certain longitude or local time.In the latter definition, EIA crests refer to the two latitudinal electron density or TEC peaks along the given longitude or local time.In our definition, a EIA crest refers to the TEC peak of an intensification region that could extend widely in longitude/ local time, and thus the northern and southern crests do not necessarily fall into the same longitude/local time.
We visualize the geographic locations of the extracted EIA crests on a map in Figure 1.Northern and southern crests are represented by blue and orange colored dots, respectively.To avoid an overcrowded figure, only the EIA crest locations at 0, 6, 12, and 18UT each day during 2003-2022 are shown.The locations of northern and southern crests track the shape of the geomagnetic equator on the geographic longitude-latitude map.At some longitudes, for example, 120°E, two concentrations of points are visible, and these correspond to the solstice latitudes of each crest.The vast majority of the northern crests are located northward of the geomagnetic equator, and most of the southern crests are located southward of the geomagnetic equator.This supports that our selected two-intensification cases can be described as TEC enhancement regions of EIAs.
For the TEC maximum of an intensification, we calculate its geomagnetic latitude, local hour, and month of year for further investigation.Following Nigussie et al. (2022), the geomagnetic latitude, ϕ, is computed using the International Geomagnetic Reference Field (IGRF) model (Alken et al., 2021) through the pyIGRF python module by where I is the geomagnetic inclination at the corresponding geographic latitude and longitude, and at 300 km altitude, approximately coinciding to peak vertical electron density.The integer local hour, H L , is calculated from the universal decimal hour, H U , and the geographic longitude, λ, by where // indicates integer division.The month of year is calculated based on what fraction of seconds in each year have passed, such that each "Month" is exactly 1/12 of the year.For convenience, we still refer to these "Months" by the corresponding Gregorian names.The above calculation of the geomagnetic latitude, local hour, and month of year are performed for all intensifications in the TEC intensification data set, including those selected as TEC enhancement regions of EIAs.

Results
To assess the statistical distribution of the EIA crest properties, we display histograms of the geographic longitude, geomagnetic latitude, local hour, and month of year of the extracted EIA northern and southern crests, in blue and orange respectively, in Figure 2.For comparisons, Figure 2 also shows the histograms for all intensifications from 2003 to 2022 in black.Data used to produce the blue and orange histograms are subsets of the data used to produce the black histograms.Figure 2a shows a wave-like longitudinal distribution of the EIA crests, peaking at approximately 160°, 90°, 10°, and 100°geographic longitudes.A similar wave-like longitudinal distribution presents in all intensification data as well, indicating that the wave-like longitudinal distribution of the crests is unlikely to be caused by biases in our selection of two-intensification cases.The interpretation of the wave-like longitudinal distribution will be discussed in Section 4. From Figure 2b, the northern EIA crests are mostly distributed between 5°and 20°in geomagnetic latitude, while the southern EIA crests are mostly located between 25°and 5°in geomagnetic latitude.These EIA crests fall within the typical range of geomagnetic latitudes where latitudinal electron density/TEC peaks from double-peaked EIA structures are commonly observed, which further verifies that our selected two-intensification cases can be treated as EIA structures.
Comparing the geomagnetic latitude histograms for the northern and southern EIA crests, the northern crests have a mean geomagnetic latitude of 11.9°with a standard deviation of 5.2°, while the southern crests have a mean geomagnetic latitude of 15.1°, with a standard deviation of 5.3°.For all intensification data, the mean geomagnetic latitude of the TEC maximum is 1.6°, slightly south of the geomagnetic equator.
Figure 2c shows histograms of the local hour.The histograms for the northern and southern crests match closely, with a mean local hour of 13.7 and a standard deviation of 1.5 hr.Most (about 99.5% of the northern crests and about 99.2% of the southern crests) of the EIA crests are distributed between 10 and 18 local hour.The local hour histogram for all intensification data is wider and peaks lower than the local hour histograms for the EIA crests, yet their peak local hours are close.For the month of year histograms shown in Figure 2d, the northern and southern EIA crests have an identical distribution over month of year because each pair is required to occur at the same universal time.The crests are notably less common in June and July, that is, northern hemisphere summer, than in other seasons.Such distribution dip is also visible in the histogram for all intensification data shown in black, but less prominent.With the 0.2 months bin size used to produce the histograms, we still have more than 1,000 data points in each bin during June -July in the histograms for the EIA crests, which ensures our later analysis on seasonal variability to be statistically significant.
Next we analyze the periodicities in the geomagnetic latitude of the EIA crests using a Lomb-Scargle periodogram of crest latitudes in universal time (Lomb, 1976;Scargle, 1982;VanderPlas, 2018).The 7-day average geomagnetic latitudes of the EIA northern and southern crests are shown as 7-day averaged timeseries in Figure 3a, along with a background color contour of the daily F10.7 index to indicate the solar cycle progression.
For both northern and southern crests, annual variation in the geomagnetic latitude are clearly notable from the time series plot: the crest moves equatorward in winter and poleward in summer.Computing the Lomb-Scargle periodogram for the full cadence data of each crest, we obtain the major periodicities in the data, shown in Figure 3b.Periods shorter than the 15 min sampling rate of the data are ruled out as non-physical.Semi-diurnal, diurnal, semi-annual, annual, and solar cycle periodicities are identified for both northern and southern crests.
Because the EIA evolution is expected to be periodic in local time, it is interesting that we find diurnal periodicity in universal time as well.The Lomb-Scargle power at each of the periodicities are listed in Table 1.We see that the southern crest has overall larger periodic power, and that distribution of power at different periodicities is asymmetrical between the crests.The dominant periodicity modes for the northern crest are semi-diurnal and annual, while for the southern crest they are diurnal and annual.The semi-annual and solar cycle periodicity modes are much weaker compared to the dominant modes.In particular, the solar cycle periodicity mode has almost vanishingly small power for the southern crest.
To analyze whether the amplitude of annual variation changes with the solar cycle, Figure 3c displays the average change from the mean geomagnetic latitude versus the average F10.7 for each solstice month, January and June,  of each year during 2003-2022.Thus, the figure shows the extrema of the annual variation in each year.The mean geomagnetic latitude is for all years of data and for northern and southern crests separately.The value of the mean geomagnetic latitude is 11.9°for the northern crest and 15.1°for the southern crest.For the winter solstice month of each hemisphere, the geomagnetic latitude change of the crest of the corresponding hemisphere has a good correlation with the F10.7.This is indicated by a Spearman correlation coefficient of 0.72 for the January northern crest and 0.47 for the June southern crest.Note that these correlations have opposite signs because annual variation moves both crests south of their mean in January and north in June, so that weaker annual variation with higher F10.7 is indicated by a positive correlation in northern winter and by a negative correlation in northern summer.The correlation is weaker for the summer solstice month of each hemisphere, with a correlation coefficient of 0.06 for the June northern crest and 0.29 for the January southern crest.In general, a larger change from the mean geomagnetic latitude is found for a lower F10.7, which indicates that the annual variation is stronger during solar minimum than during solar maximum.The weaker correlation for the summer solstice month of each hemisphere compared to the winter solstice month of each hemisphere shows that the solar cycle effect on the annual variation has a seasonal component, and is strongest in the winter of each hemisphere.
Below we further investigate the dominant periodicity modes, including annual, diurnal and semi-diurnal variations in the geomagnetic latitudes of EIA crests, and explore the solar cycle effect on these variations.Figure 4a shows the annual variation in the geomagnetic latitude.Both crests move southward during the northern hemisphere winter and northward during the northern hemisphere summer-that is, poleward in local summer and equatorward in local winter.The geomagnetic latitudinal range of the annual variation is asymmetrical between the crests: the southern crest latitude varies about 10°, between approximately 20°at January -December and 10°at July, while the northern crest latitude varies about 6°, between 10°at January -December and 16°at July.Because of the asymmetrical "motion" of the crests, the distance between them fluctuates over the months, between about 30°at January -December and about 26°at July.The annual variation is most pronounced in solar minimum years (2007-2009 and 2018-2020) and least pronounced in solar maximum years (2012)(2013)(2014), with the difference between solar minimum and maximum at most about 4°in both hemispheres.
The diurnal and semi-diurnal variations in universal time of the crest geomagnetic latitudes are visualized in Figure 4b.Both northern and southern crests dip southward near 15UT at which time Northern (Southern) crests are on average at 16°( 7°) longitude with a standard deviation of 12°(13°), and the northern crest has an additional southward dip at about 2.5UT, at which time it occurs on average at 65°longitude, with large (153°) spread.The single-dipped structure of the southern crest's latitudinal variation corresponds to the diurnal variation identified earlier with the Lomb-Scargle periodogram, which tracks universal time periodicity.The two-dipped structure of the northern crest's latitudinal variation clearly shows the semi-diurnal variation, which is much less pronounced for the southern crest.The solar cycle has a slight effect to move both crests northward at solar maximum and southward at solar minimum, except between about 15UT and 20UT, when the Northern (Southern) crests on average occur at 91°( 94°) longitude with a standard deviation of 20°(23°), where the effect is reversed.While the southward dips near 15UT for both crests are not impacted by the solar cycle, the southward dip near 2.5UT for the northern crest is slightly more profound during solar minimum than solar maximum.We also track the geomagnetic latitude of the crests in local time (LT).Figure 4c shows the average geomagnetic latitudes at given local times.During each day, the northern (southern) crest moves between 9°( 11°) at 10LT when they are first observed to 12°( 16°) when they are most often observed at 14LT, and finally to 12°( 14°) at 18LT.Solar cycle effect is minimal, but where present moves especially the northern crest poleward in solar maximum and equatorward in solar minimum.The maximum separation between solar maximum and minimum geomagnetic latitude for the northern crest is about 2°, which occurs between 12 and 14LT.
Significant periodic power in semi-diurnal and diurnal variation in universal time is interesting, as it is known that the formation and evolution of EIA crests depends on local time and thus the diurnal periodicity of EIA crests is typically addressed in the local time frame.The periodicity in universal time can be explained in terms of a standing longitudinal structure, which the crests move across as the Earth rotates.Below we show that the semidiurnal and diurnal periodicity can be attributed almost completely to the longitudinal distribution of crests' geomagnetic latitudes.Figure 5a shows the distribution of the geomagnetic latitude for given geographic longitudes, essentially a map of the EIA crest locations.Figure 5b shows the average crest geographic longitude for each 15-min universal time bin during a day.Because the crests typically occur around 14LT, the rotation of the Earth sees the EIA dragged around the globe each day.The universal time may thus act as a proxy for the longitude of the crests.If the diurnal/semi-diurnal variations of the crests' geomagnetic latitudes can be explained by the longitudinal structure in Figure 5a, we should be able to reproduce the variations based only on the geomagnetic latitude for each geographic longitude and the geographic longitude for each universal time.Figure 5c does this, where the mean geomagnetic latitude for geographic longitudes within the standard deviation (as shown in Figure 5b) is plotted, with error bars giving the standard deviation of the geomagnetic latitude in each bin.In a sense Figure 5c plots the geomagnetic latitude versus universal time "parameterized" by the geographic longitude.Figure 5c reproduces the variation characteristics in Figure 4b well, in particular the dips around 15UT and the dip around 2.5UT for the northern crest, indicating that the diurnal/semi-diurnal variations in universal time are really variations by longitude and can be largely attributed to the crests' longitudinal structure.

Annual and Semi-Annual Variations
We identify the common dominant mode of temporal variation in the geomagnetic latitude for both northern and southern EIA crests to be annual.Both crests move poleward in local summer and equatorward in local winter,

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that is, toward the summer hemisphere (Figure 4a).The southern crest exhibits a larger extent of latitudinal variation than the northern crest.These results reproduce the annual variation trends reported for particular longitudinal sectors (Tsai et al., 2001;L. Huang et al., 2013;J. Liu et al., 2020;Mo & Zhang, 2021) and for an extended longitudinal range (Eastes et al., 2023).Recall that in our study, an EIA crest is defined as the maximum TEC within a TEC intensification region, hence the crest corresponds to the latitudinal and longitudinal peak in TEC.The inclusion of the longitudinal dimension for the EIA crests indicates that the identified annual variation is a global phenomenon.Previous authors (L.Huang et al., 2013;J. Liu et al., 2020;Mo & Zhang, 2021) suggest that interhemishperic asymmetry in the annual latitudinal variation for certain longitudes could be due to displacement of the magnetic equator from the geographic equator, which causes asymmetrical effects of the transequatorial neutral wind.Based on the distribution of longitudes we observe (Figure 2a), the majority of crests (71.5% of north crests and 73.4% of south crests) occur at longitudes where the geomagnetic equator is north of the geographic equator, which is known to be related to stronger annual variation in the Southern crest.This may cause the larger variation power we observe for the Southern crest.Tsai et al. (2001) suggests that the annual variation could be explained by the combined effect of the meridional neutral wind blowing from summer to winter hemisphere, the subsolar point, and the auroral equatorward wind (Millward et al., 1996).Modeling results of Abdu (2005) and Nanan et al. (2012) suggest that the meridional wind can move the crests upwind in an EIA structure, yet the physical mechanism is unknown.The upwind motion of the crest latitudes is consistent with observations for the American sector by J. Liu et al. (2020).Our result indicates that both crests move toward the subsolar point over the months (Figure 4a), and the direction of the motion is against the prevailing summer-towinter meridional wind direction.Such motion is more prominent during solar minimum than solar maximum.This implies that the auroral equatorward wind, driven by solar wind/magnetosphere energy deposition into the thermosphere, may not be a dominant factor contributing to the annual variation, as solar maximum years typically correspond to more active geomagnetic conditions than solar minimum years, and thus more energy deposition into the thermosphere and stronger auroral equatorward wind.
We find that the amplitude of the annual variation has a linear relationship with the F10.7 index.Stronger annual variation occurs with a smaller F10.7, especially for the winter hemisphere (Figure 3c).As a result, the annual variation of the crests' latitudes is more pronounced in solar minimum than solar maximum, and the difference between solar minimum and maximum is more visible in local winter than in local summer (Figure 4a).Our result shows similar general features to the results of J. Liu et al. (2020) over the American sector and of L. Huang et al. (2013) around 110°E longitude.The effect of the meridional neutral wind should be more noticeable in solar minimum, because the equatorial plasma fountain is weaker with less ionization.We might expect this to be most true in winter when there is lower exposure to solar radiation.
Several authors have reported semi-annual variation of the crest latitudes in the Asian sector, with more poleward crests around equinoxes than solstices, which is sometimes attributed to high thermal pressure in the sector during the summer solstice, or the semi-annual variation of the equatorial zonal electric field strength (C.-C.Wu et al., 2008;Zhao et al., 2009;Mo et al., 2018;J. Liu et al., 2020;Mo & Zhang, 2021).The periodogram we compute also reveals semi-annual periodicity mode, but it is much lower power than the annual variation in either crest (Table 1)-8.7% and 25% of the annual variation power for the northern and southern crests, respectively.The low power of the semi-annual variation suggests that it is not the dominant trend compared to the annual variation.Considering our definition of crests has taken into account the longitudinal dimension, our result implies that the semi-annual variation is not global and perhaps only present at certain longitudes (such as the eastern Asian sector, where it has been reported).This is supported by the lack of semi-annual variation of the crest latitudes in the American sector (J.Liu et al., 2020).
We also notice an annual variation in the occurrence of the EIA crests, which appear less often during summer of the northern hemisphere, as shown in Figure 2d.This annual variation in the distribution has two causes.First, for all two-intensification cases from the 20-year TEC intensification data set, they occur less often during summer than other three seasons of the northern hemisphere (Meng & Verkhoglyadova, 2023), leading to a smaller data pool in June -August to select the double-peaked EIAs from.The less two-intensification cases during northern hemispheric summer than other three seasons is due to semi-annual variation and annual asymmetry in the number of TEC intensifications per TEC map (Meng & Verkhoglyadova, 2023).Such variation and asymmetry is visible from the histogram of all intensification data over month of year shown as black in Figure 2d, which peaks around equinoxes and dips around solstices, and dips the lowest around June solstice.Second, in our selection of the double-peaked EIAs, more two-intensification cases during northern hemispheric summer than during other seasons are ruled out due to their longitudinal distance exceeding the criterion of 45°.The excluded twointensification cases could be latitudinally single-crest events (L.Huang et al., 2014;Fathy & Ghamry, 2017;Loutfi et al., 2022;Hussien et al., 2023), which were also found to occur more often around June solstice than other time of year (L.Huang et al., 2014;Fathy & Ghamry, 2017).

Diurnal/Semi-Diurnal Variations and Longitudinal Structure
We report diurnal and semi-diurnal variations of the EIA crests' latitudes in universal time, which has not been previously shown.Large periodic power in universal diurnal and semi-diurnal modes is interesting, because many of the drivers of the ionosphere depend on local time such that the formation and evolution of EIA crests mainly progresses in local time.We show in Figure 5 that the universal day variation of the crests can be reproduced considering the most probable longitude at each time, and the most probable latitude at each longitude.We can thus attribute the diurnal and semi-diurnal variations in universal time to the EIA rotating around the Earth and exhibiting different parts of the longitudinal structure of the crests' latitudes at different universal times.Our result does not indicate that the development of the crests depends on universal hour, but does reveal that the longitudinal structure is important for the "daily" (i.e., within one rotation period) movement of the EIA.The EIA crests' geomagnetic latitudes display wave-like structure across the geographic longitudes (Figure 5a), which shares similarities with the sinusoidal patterns of EIA crest locations in geographic longitude versus geomagnetic latitude coordinates reported by Nigussie et al. (2022), for instance the peak around 100°longitude for the north crest, the peak around 80°longitude for the south crest, and the dip around 0°longitude for the south crest.However, the wave-like structure does not fully agree with Nigussie et al. (2022).The discrepancy could be caused by differences in the observational data and the identification of EIA crests: our study uses global TEC data from 2003 to 2022 while Nigussie et al. (2022) used NmF2 extracted from electron density profiles and insitu ion density data within 12-15 LT only from 2013 to 2019; the northern and southern crests in our study could be longitudinally separated as large as 45°while the northern and southern crests in Nigussie et al. (2022) are aligned within 8°longitudinal sectors.The sinusoidal oscillation in the longitudinal distribution of the EIA crest latitudes is known as the wave-number-four longitudinal structure, which is thought to be produced by atmospheric tidal winds in the E-layer that affect the zonal electric field through the neutral wind dynamo process, in turn modifying the equatorial plasma fountain (England et al., 2006;Immel et al., 2006;Sagawa et al., 2005).The longitudinal wave-like structure we report here reflects the wave-number-four structure to some extent, which implies the contribution of atmospheric tidal forcing to the wave-like structure.
The wave-number-four longitudinal structure of EIAs is usually observed at fixed local time and can show up in several physical parameters associated with the crest magnitude and latitudinal location.Interestingly, our result reveals a four-peaked longitudinal distribution of the EIA crest occurrence (Figure 2a) that is similar to the known wave-number-four structure.Considering the local hour distribution of our selected EIA crests maximizes between 13 and 15LT (Figure 2c), we compare the longitudinal distribution of the EIA crest occurrence to the wavenumber-four longitudinal structure of the TEC magnitude during 12-14LT and 14-16LT presented by Lin, Hsiao, et al. (2007), and find the peak/dip longitudes coincide well.Therefore, it is highly possible that the four-peaked longitudinal distribution of the EIA crest occurrence is yet another manifestation of the wave-number-four structure of EIAs.
Local time evolution of the crests' latitudes is also presented (Figure 4c).We find that the northern (southern) crest has already formed at 10LT, located at 9°( 11°) geomagnetic latitude.The crests move poleward and reach their maximum separation of 28°at 14LT, and then persist at similar latitudes until 18LT at least.The latitudinal motion of the crests in local time has been previously observed for limited temporal and/or longitudinal extents (Lin, Liu, et al., 2007;Loutfi et al., 2022;Mo et al., 2018;Yeh et al., 2001).Our result agrees with the previous studies in general, although in past results the crests receded slightly more strongly toward the equator at dusk.As suggested by Yeh et al. (2001), the local time evolution of the crest latitudes correlates with the diurnal variation of the EEJ strength, and thus the crests' diurnal motion could be fundamentally controlled by the equatorial zonal electric field.

Conclusions
Temporal variation of the EIA crest latitudinal locations has been previously reported, typically over small longitudinal or local time extents.This work gives the first statistical analysis, to our knowledge, of the temporal variation of EIA crest locations viewed globally and spanning about two solar cycles.We utilized a 20-year TEC intensification data set obtained from the JPLD GIM data product and extracted double-peaked EIA structures from the data set.When maps had two regions of enhanced TEC which were less than three local hours separate, we characterized these TEC enhancements as "intensification regions" corresponding to double peaked EIAs.The TEC maximum within an intensification region was taken as the EIA crest.For all EIA crests during 2003-2022, we examined the statistical distribution of the crest location and occurrence time, identified temporal periodicity modes in the crest latitude, investigated dominant temporal variations of the crest latitude, and explored the solar cycle effect on the latitudes.Our major results are • The geomagnetic latitude of both the northern and southern crests exhibits semi-diurnal, diurnal, semi-annual, annual, and solar cycle periodicity modes.The dominant periodicity modes are annual and semi-diurnal for the northern crest, while the dominant periodicity modes are annual and diurnal for the southern crest.Semiannual and solar cycle modes are significantly weaker than the dominant modes.• Annually, the geomagnetic latitude of each crest moves toward the poles in local summer and toward the equator in local winter.The variation is stronger for the southern crest than the northern crest.These properties of the annual variation match with previous results for limited longitudinal sectors, indicating that the annual variation is a global phenomenon.The solar cycle modulates the annual variation in the way that the strength of the annual variation linearly correlates with the F10.7 index.Stronger annual variation is found at smaller F10.7, especially for the winter hemisphere.• In universal time, diurnal and semi-diurnal variations of the crest geomagnetic latitude are characterized by both northern and southern crests dipping southward near 15UT, when Northern (Southern) crests occur at mean 16°( 7°) longitude with a standard deviation of 12°(13°), and the northern crest additionally dipping southward near 2.5UT, when it is on average at 65°longitude, with large (153°) spread.The solar cycle does not impact the dips at 15UT but slightly modifies the amplitude of the dip at 2.5UT for the northern crest.The diurnal and semi-diurnal variations can be possibly attributed to the known wave-number-four longitudinal structure of EIAs.The wave-number-four structure very likely also manifests itself as the four-peaked longitudinal distribution of the EIA crest occurrence we report for the first time.Our results imply the importance of the lower atmospheric tidal modulation on the ionospheric longitudinal structuring.• In local time, the crests form earlier than 10LT and move poleward to their maximum separation distance at 14LT, persisting at these latitudes until at least 18LT.The solar cycle does not affect the motion of the southern crest, but minimally changes the motion of the northern crest during 12-14LT, so that the latitudinal separation between the northern and southern crests is 2°more during solar maximum than solar minimum.
For the first time long-term variability of the latitudinal and longitudinal crest locations for the classical doublepeaked EIAs was analyzed globally, revealing dominant modes of the northern and southern crest variability.
While we focus on characterizing the crest location in this study, the crest magnitude is another key parameter representing EIA characteristics and can be addressed in a follow-on study.Furthermore, as the EIA TEC enhancement regions can have a large longitudinal extent, future investigation on the longitudinal variation of the TEC within the enhancement regions for consecutive TEC maps is warranted.Statistical properties of nonclassical EIAs, for instance single-peak and three-peak EIAs, can be extracted from the 20-year TEC intensification data set and are subjects of future studies.

Figure 1 .
Figure 1.The geographic locations of the EIA crests at 0, 6, 12, and 18 UT each day from years 2003 to 2022, extracted from the TEC intensification data set.The northern crests are represented by blue dots, while the southern crests are represented by orange dots.

Figure 2 .
Figure 2. Histograms for (a) the geographic longitude with 3°bins, (b) the geomagnetic latitude with 1°bins, (c) the local hour with 15 min bins, and (d) the month of year with 60 bins, respectively for the point of maximum TEC in each intensification region.Histograms of all intensifications from the 20-year TEC intensification data set are shown in black.For the extracted crests in two-crest EIAs from 2003 to 2022, histograms of the northern crests are shown in blue, while histograms of the southern crests are shown in orange.

Figure 3 .
Figure 3. (a)The 7-day average geomagnetic latitude of the northern crest in blue and the southern crest in orange is plotted by date, with color-shaded area showing the standard deviation of geomagnetic latitudes in each 7-day bin.The horizontal black dashed line marks the geomagnetic equator.The background of the plot is a color contour of the 120-day running averaged F10.7 value to show the progress of solar cycles.The corresponding colorbar is displayed on the right.(b) Lomb-Scargle periodograms calculated from the full cadence data are shown for the geomagnetic latitude of the northern EIA crest (blue, above) and the southern EIA crest (orange, below).Dotted, dot-dot-dashed, dash-dotted, dashed, and solid lines respectively mark periods of 0.5 days, 1 day, 0.5 years, 1 year, and 11 years.(c) A scatter plot shows the average change from 20-year-mean geomagnetic latitude for each year January and June by the average F10.7 in that month.Blue circles and blue triangles mark the northern crests for January and June respectively, while orange circles and orange triangles represent the southern crests in January and June respectively.Error bars mark the standard deviation along both axes.The Spearman correlation coefficients are given in the legend.

Figure 4 .
Figure 4.The average geomagnetic latitude in each bin is shown for the EIA crests, versus the month of year with 0.2-month bin size (a), the universal hour with 15-min bin size (b), and the local hour with 15-min bin size (c), respectively.For both northern and southern crests, all data are shown in gray, data from solar minimum years 2007-2009 and 2018-2020 are shown in green, and data from solar maximum years 2012-2014 are shown in red.Error bars mark the standard deviation in each bin.In all panels, the horizontal black dashed line marks the geomagnetic equator.The orange dotted line in (a) represents the mean location of the sub-solar point, with the yellow shading giving the range.

Figure 5 .
Figure 5. (a) Averages of the geomagnetic latitude, binned by geographic longitude with 3°bin size.(b) Averages of the geographic longitude, binned by universal time with 15-min bin size.(c) The mean geomagnetic latitude for all geographic longitudes within the standard deviation in each 15-min universal time bin (as shown in (b)).Error bars represent the standard deviation of the data in each bin.

Table 1
Power at Peaks in Geomagnetic LatitudeLomb-Scargle Periodogram DUNN ET AL.