Using radio occultation-based electron density profiles for studying sporadic E layer spatial and temporal characteristics

Abstract

An improved method for identifying sporadic E (Es) layer properties from radio occultation (RO) electron density profiles (EDPs) is presented. The data used are sourced from COSMIC-1 RO EDPs collected between 2006 and 2019, which cover altitudes from 75 to 145 km. Initially, we evaluate the reliability of EDPs using the International Reference Ionosphere 2016 (IRI-2016) model and select only those profiles with a reliability score of 0.6 or higher (on a scale up to 1) for further analysis. Preliminary Es layer inversion results are obtained and validated against electron density data derived from ionosonde fbEs measurements, demonstrating a linear correlation with a coefficient of 0.72 and a mean absolute percentage error of 36.08%. Further verification using RO S4max data shows that this research method achieved an accuracy of 85.3% in identifying Es events. We perform a detailed analysis of Es layer relative occurrence rates, intensity, and thickness. The Es intensity is expressed by NmμEs (the layer’s maximum electron density (Nm) corresponding to the metal (μ) ion), which is estimated from the measured layer peak electron density NmEs by subtracting the ambient E region electron density NeE(hEs) at the height of the layer’s peak hEs, computed from the IRI-2016 model. Our findings reveal that Es layers predominantly occur in mid-latitude regions during summer, with average intensities between $5\times {10}^{4 }\text{ and }8\times {10}^{4 }\text{el}/{\text{cm}}^{3}$. The most likely thickness of Es layers is approximately 1.4 km. Additionally, the present study shows that because NeE(hEs) increases during daytime, which leads to increases in NmEs, confirming that NmμEs is the proper parameter for assessing the Es layer intensity, in line with what is suggested by Haldoupis et al. (Haldoupis et al., J Atmos Sol Terr Phys 206:105327, 2020).

Graphical Abstract

1 Introduction

The sporadic E (Es) layers occur frequently in the 90–130 km altitude range of the E region ionosphere, becoming denser in the summer months and during the daytime. They are made of long-lived metal ions of meteoric origin, having typical thicknesses of a few kilometers and horizontal extensions of hundreds of kilometers (e.g., see review by Whitehead 1989). The Es intensities and occurrence rates exhibit pronounced seasonal variations and geographical distribution differences (Haldoupis et al. 2007; Arras et al. 2008; Yu et al. 2019). In addition, Es layers may impact severely radio communication and navigation. It is suggested that about one-third of the ionospheric weather-related interruptions in the Global Navigation Satellite System (GNSS) signals are attributable to pronounced Es layer activity (Yue et al. 2016; Yu et al. 2021). Knowledge about the global Es variability contributes to radio communication applications and the researches related to space weather and ionospheric climatology.

One of the fundamental tasks in Es layer studies is to obtain reliable estimates of the basic parameters characterizing Es, which include the Es layer occurrence rate (Es OR), the layer intensity, layer altitude, and layer thickness. Among them, the most important parameter is the layer intensity which is identified with the metal ion content inside the layer. So far, the most common observational parameters used to estimate the Es layer intensity are the ionosonde-measured critical reflection frequency foEs and the blanketing frequency fbEs (e.g., see Whitehead 1989), whereas for radio occultation (RO) studies are the S4 index and signal-to-noise ratio (SNR) amplitudes (e.g., see Arras and Wickert 2018; Yu et al. 2019; Niu et al. 2019a, b). These Es intensity estimates are not as accurate as they could be because of inherent measurement uncertainties. For example, the ionosonde-based foEs (and fbEs) values which are used to measure the layer electron density include in addition to the metal ion (electron) density the ambient E region electron (ion) density associated with regular solar photoionization. The regular E region electron contribution in sporadic E has been ignored till recently when Haldoupis (2019) and Haldoupis et al. (2020) showed that foEs significantly overestimates Es intensities during the daytime, more severely when the layers are weak. These authors suggested a method to correct this bias by obtaining a critical frequency, foμEs, that corresponds to the layer’s metal (μ) ion density only, which turned out to be an improved measure of Es intensity. On the other hand, the more recent S4 index and S4max estimates used in RO studies to quantify Es intensities are also of limitations because these values only indicate the intensity of signal fluctuations rather than the electron density values.

The present paper deals with RO E region measurements to study sporadic E properties. In the past RO sporadic E studies, the Es-related parameters were mostly derived from SNR profiles in the E region (Arras et al. 2008; Chu et al. 2014; Xu et al. 2022), the S4 index profiles (Yu et al. 2019; Luo et al. 2021), or the total electron content (TEC) profiles (Niu et al. 2019a, b). On the other hand, the routinely estimated RO electron density profiles (EDPs) that can provide a direct estimate of Es electron density, were seldom utilized because they are at times highly incorrect. Dou et al. (2010) is the only study that used RO EDPs to compute Es layer occurrence rates (Es ORs), which did not concern about Es electron densities. In the present work, the method of Dou et al. (2010) is improved so that in addition to Es ORs, the analysis was expanded to investigate sporadic E layer statistics that included variations in layer intensity and thickness. Note that the regular E region electron contribution in sporadic E is corrected when deriving the layer intensity. This study aims to validate the RO EDP method for Es layer analysis and to examine the spatiotemporal properties of the Es layers detected based on it. This is achieved by comparing the retrieval results with those from the International Reference Ionosphere (IRI-2016) model, ionosonde data, RO S4max data, and existing literatures.

2 Radio occultation measurements

The Formosa Satellite-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1), launched in April 2006, is a significant RO project. By the end of 2019, it had accumulated over 4 million RO EDPs for the COSMIC Data Analysis and Archive Center (CDAAC). The ionPrf data product, one of COSMIC-1's Level-2 ionospheric retrieval products, provides the RO EDPs inverted from individual occultation events by applying the onion-peeling method. These EDPs present the ionospheric electron density below the LEO satellite altitudes. Detailed calculations and the technical document for deriving the ionPrf product (unpublished manuscript) can be found at https://cdaac-www.cosmic.ucar.edu/cdaac/doc/documents/gmrion.pdf. Validation of these profiles against ionosonde measurements for the F region’s peak density (NmF2) revealed a root mean square error (RMSE) of roughly 10–20% for NmF2 (Pedatella et al. 2015). However, significant errors in the RO EDPs at E region altitudes arise due to the spherical symmetry assumption in the EDP inversion process (Lei et al. 2007; Yue et al. 2010). Wu et al. (2015) noted that these errors could reach up to 100% in the E region when substantial horizontal gradients occur in the F region. Without calibration, these errors would lead to systematic inaccuracies in ionospheric climatological studies (Lei et al. 2010; Liu et al. 2010; Yue et al. 2012). Pedatella et al. (2015) improved the Abel inversion method by using information on the horizontal gradients based on COSMIC observations, reducing the primary error associated with the standard approach. The ionospheric product calculated by this improved method is named igaPrf and is now also released as COSMIC-1’s Level-2 ionospheric retrieval products. Both ionPrf and igaPrf products are accessible through the CDAAC at https://cdaac-www.cosmic.ucar.edu/cdaac/tar/rest.html.

In the study of Pedatella et al. (2015), an analysis was performed comparing the March monthly median electron density values at 100 km as observed by the ionPrf and igaPrf data products across different years. Following their methodology, we conducted a comparative analysis of the ionPrf and igaPrf data for various Es layer altitudes over the period 2006–2019, as illustrated in Fig. 1. This figure compares the median electron density values obtained from the ionPrf (displayed in the first column panels) and igaPrf (shown in the second column panels) data products, along with their differences (presented in the third column panels). The altitude of the data in each row of panels is marked on the right side of Fig. 1. Although results are only presented for altitudes of 100, 110, 120, and 130 km, these results can be considered as representative of the general behavior of different inversion methods at Es layer altitudes. Our findings at the 100 km altitude are in broad agreement with Fig. 4 of Pedatella et al. (2015). Taking the results at 100 km as an example, significant disparities in electron density values between the two data products are most pronounced at low latitudes, where maximum difference exceeds $\pm 0.5\times {10}^{5} e\text{l}/{\text{cm}}^{3}$, approximately one-third of the observed values. The differences in electron density distribution characteristics between the two data products are evident in two aspects. First, the ionPrf data show the presence of three electron density maxima at low latitudes during daytime, characteristic of the artificial plasma cave resulting from the assumption of spherical symmetry (Liu et al. 2010; Yue et al. 2010). Conversely, the igaPrf data at 100 km depict an almost complete elimination of the equatorial maximum. Second, regions of negative electron density, marked by black contours in Fig. 1, are significantly reduced at low latitudes in the igaPrf data, indicating an improvement for the igaPrf data at 100 km altitude. However, the igaPrf data exhibit larger regions of negative nighttime electron densities between about 40° to 60° magnetic latitude. This slight error at these latitudes during nighttime is attributed to the significant day-to-day variability in the nighttime ionosphere at middle latitudes (Rishbeth and Mendillo 2001), which contradicts the assumption of a constant electron density gradient within a month employed in the improved Abel method of the igaPrf data product (Pedatella et al. 2015). Finally, regarding other Es layer altitudes, the discrepancy characteristics between the two products are similar to those observed at 100 km, although there are variations in the magnitude of electron density values.

Fig. 1

Geomagnetic latitude versus local time distribution of median electron densities at different altitudes from 2006 to 2019. The first column panels show median electron densities from ionPrf data; the second column panels present those from igaPrf data; the third column panels highlight the differences between these two datasets. Black contour lines indicate zero electron density values. The grid resolution in the figure is ${5}^{\circ }\times 1h$

Despite some shortcomings, the igaPrf data have made significant progress in reducing the systematic errors caused by the spherical symmetry assumption, especially in eliminating artificial “plasma caves” and reducing occurrences of negative electron density values. Sakib et al. (2023) further indicated that the igaPrf product provides accurate measurements of electron density in the ionospheric E-region, and they employed E-region EDPs from the igaPrf product to validate the results from the Atmospheric Ultraviolet Radiance Integrated Code (AURIC). As shown in their Fig. 4, the average differences between the E-region electron density profiles obtained from igaPrf and those computed by high-resolution AURIC are less than $0.5\times {10}^{5} e\text{l}/{\text{cm}}^{3}$. In summary, the enhanced accuracy of the igaPrf product offers more reliable EDPs for ionospheric studies at E-region altitudes, making it suitable for research focused on this region. In this study, we analyze the spatiotemporal distribution of Es layers using EDPs from COSMIC-1 igaPrf files, spanning from day 112 of 2006 to day 365 of 2019. For effective Es layer analysis, it is crucial that the EDPs cover the E-region altitudes (75–145 km). EDPs meeting this criterion are referred to as E-region EDPs.

Figure 2 depicts the geographical distributions of all EDPs (upper panel, total: 4,619,526) and E-region EDPs (lower panel, total: 3,976,631), derived from COSMIC-1 RO igaPrf files. The quantity of E-region EDPs is notably lower than the total observed EDPs, attributable to some EDPs not extending to E-region altitudes. However, the distribution patterns of both datasets are almost similar, showing a higher density in mid-latitude areas (especially around 50° and 20° latitudes), a gradual decrease near the equator, and a notable scarcity in polar regions. This distribution of EDPs aligns with the spatial distribution patterns of COSMIC-1 observations reported by Chu et al. (2014) and Chu et al. (2021). Additionally, the geometric distribution of COSMIC-1 LEO satellite trajectories presented by Cheng et al. (2021) reveals a denser concentration of satellite trajectory lines in mid-latitude regions, which further corroborate our observations. Therefore, this spatial distribution characteristic of EDPs and other COSMIC-1 observations is primarily a result of the geometric constraints imposed by the satellite constellation’s orbital configurations, which include an orbital inclination of 72° and altitudes of around 800 km. Due to the limited E-region EDP data in polar areas, our analysis focuses on the ${70}^{\circ }$ S–${70}^{\circ }$ N region, which includes 3,569,266 EDPs. In this study, subsequent mentions of E-region EDPs exclusively refer to EDPs within this specified latitudinal range.

Fig. 2

The global distribution of the number of electron density profiles (EDPs) from igaPrf files released by the COSMIC-1 occultation mission during the period 2006–2019. The upper panel shows the total number of EDPs, while the lower panel shows the number of E-region EDPs. The data resolution is ${5}^{\circ }\times {5}^{\circ }$

3 Reliability analysis and data screening of the E-region electron density profile

The IRI-2016 model is recognized as the official standard for the ionosphere by the International Standardization Organization (ISO), capable of providing predictions at various altitudes within the range of 50 km to 2000 km (Bilitza et al. 2017). In the study of three-dimensional ionospheric electron density modeling at low latitudes, Yang and Fang (2023) used simulation values from the IRI-2016 model at altitudes of 100–150 km to replace the corresponding COSMIC-1 observation values due to the higher reliability of these simulations. Furthermore, Haldoupis (2019) highlighted that various validation studies regarding the accuracy of the IRI model’s electron densities demonstrate its capability in producing fairly realistic E region electron density profiles at mid-latitudes from about 100 to 140 km, where sporadic E layers are mostly located. Therefore, to evaluate the E-region EDPs, we compare them to electron density values at identical spatiotemporal points simulated by the IRI-2016 model. The assessment employs two statistical metrics: the weighted normalized root mean square error (WNRMSE) and the Pearson correlation coefficient (r). Specifically, for each E-region EDP, the calculation of WNRMSE follows Eqs. (1) to (3):

$${\text{WNRMSE}}=\frac{\text{WRMSE}}{{\text{AD}}},$$

(1)

where

$${\text{WRMSE}}=\sqrt{\frac{{\sum }_{i=1}^{n}{w}_{i}{\left({C}_{i}-{O}_{i}\right)}^{2}}{{\sum }_{i=1}^{n}{w}_{i}},}$$

(2)

$${\text{AD}}=\frac{\left({O}_{max}-{O}_{min}\right)+\left({C}_{max}-{C}_{min}\right)}{2}.$$

(3)

Here, AD represents the average deviation used for normalization. The weight ${w}_{i}$, assigned to the $i{\text{th}}$ data point in the profile, is adjusted by altitude. Specifically, in the altitude range of 90–130 km, where the Es layers are prominent, ${\text{w}}_{\text{i}}$ is assigned a value of 0.1 to account for complex Es layer variations that can cause significant discrepancies between the RO-observed values and the IRI-calculated ones. This adjustment addresses the significant discrepancies between RO observations and IRI-2016 model calculations attributable to the influence of Es layers. The IRI-2016 model lacks a probability model for Es layer occurrences, as highlighted by Bilitza (2018), leading to expected discrepancies in observed electron density values at Es layer altitudes compared to IRI predictions. Consequently, a reduced weight of 0.1 (an empirical threshold) is applied to diminish the Es layers’ influence. For the other altitudes in the height range of 75–145 km, ${\text{w}}_{\text{i}}$ is set to 1. ${C}_{i}$ and ${O}_{i}$ represent the IRI-calculated and the RO-observed electron density for the $i{\text{th}}$ data point, respectively. ${C}_{max}$, ${C}_{min}$, ${O}_{max}$, and ${O}_{min}$ represent the extreme data points in either the model-calculated or the RO-observed profile, and $n$ denotes the total number of data points.

The Pearson correlation coefficient evaluates the linear relationship between the IRI-calculated electron density values and the RO-observed ones by using Eq. (4):

$$r=\frac{{\sum }_{i=1}^{n}\left({C}_{i}-\overline{C }\right)\left({O}_{i}-\overline{O }\right)}{\sqrt{{\sum }_{i=1}^{n}{\left({C}_{i}-\overline{C }\right)}^{2}}\sqrt{{\sum }_{i=1}^{n}{\left({O}_{i}-\overline{O }\right)}^{2}}},$$

(4)

where $\overline{C }$ and $\overline{O }$ represent the mean values of the IRI-2016 model and occultation data, respectively.

Based on the WNRMSE and the Pearson correlation coefficient (r), we introduce a composite metric comprehensively evaluating the reliability of an E-region EDP, which is calculated as the score in Eq. (5):

$${\text{score}}=0.3\times r+0.7\times \left({1}-{\text{WNRMSE}}\right).$$

(5)

This equation takes into account both the correlation $r$ and the WNRMSE error, with the coefficients 0.3 for $r$ and 0.7 for WNRMSE determined through a trial-and-error process. These weights reflect the relative importance of WNRMSE compared to $r$ in this context. As explained, WNRMSE takes into account the possible significant discrepancies between observations and model simulations aroused by complex Es layers and assigns different weights for different altitude ranges, whereas $r$ does not distinguish between heights, making the former parameter more important for the score outcome.

In Fig. 3, the blue lines depict E-region EDPs, whereas the red lines illustrate IRI-2016 model calculations in the same space–time conditions. Each panel's header details the LEO satellite ID, time (year, day of year, universal time), and the associated obscured GNSS satellite ID. Each panel also displays a reliability score, derived from Eq. (5), representing the E-region EDP’s reliability. As this score increases, the percentage difference between the observed and the modeled values decreases, indicating better consistency between them. Based on the data volume and reliability assessments, a threshold score of 0.6 is established and profiles scoring below this threshold are omitted. Consequently, 1,524,861 profiles, representing 42.7% of the total EDPs from the E-region EDP dataset, are retained for further analysis.

Fig. 3

Comparisons between the RO-observed electron density profiles (blue curves) and the IRI-calculated ones (red curves). The panels are sorted in ascending order of reliability scores, with higher scores indicating smaller differences between the profiles in the panels. The title of each panel displays the identifier of the RO event

4 Methods for extracting Es layer parameters

Our statistical analyses about the vertical resolutions of RO EDPs suggest an average resolution of 2.5 km, with poorer cases diminishing to resolutions of 6 km. Considering that the thickness of the Es layer generally ranges from 0.6 to 2.0 km (Whitehead 1989), such resolution is insufficient for accurately calculating the Es layer thicknesses. Therefore, there is a need to enhance the vertical resolution of the original data. The first step involves interpolating EDPs at 0.1 km vertical intervals using spline interpolation. Following this, the background electron density is determined through a least squares quadratic fit, from which the enhancement factor is calculated. This factor is defined as the ratio of the sporadic peak to the background value, aligning with the methodology of Dou et al. (2010). In their research, an RO event is identified as an Es event if the enhancement factor is equal to or greater than 2.0. However, incoherent scatter radar observations indicate that the electron density of Es layers can sometimes drop below $1\times {10}^{4} \text{el}/{\text{cm}}^{3}$, as exemplified in Figs. 2 and 3 of Mathews (1998), with magnitudes that can even fall below the peak levels of the conventional E layer. To identify more of these weaker Es layers, this paper sets the minimum enhancement factor threshold as 1.5. Due to the adoption of a lower threshold, to prevent misidentification, an additional criterion for Es layer identification is introduced. Specifically, for an RO-observed peak density to be identified as an Es event, it must surpass the electron density at the same altitude provided by the IRI-2016 model. This criterion ensures that the detected Es layer represents an actual enhancement in ion density. In an Es event, the layer's altitude is marked by the peak electron density altitude. When multiple peaks within 90–130 km meet Es layer criteria, only the one with the highest factor is considered for Es layer inversion.

Figure 4 demonstrates the detailed methodology for identifying Es layers through four exemplar EDPs. Each panel displays its geographical location and local time (LT). We categorize event-1 and event-2 as non-Es layer events due to an enhancement factor below 1.5 and an electron density peak under the IRI-2016 model's value, respectively. In contrast, event-3 and event-4 are categorized as Es layer events, as they fulfill the predefined criteria for enhancement factors and electron density peaks. Note that in Fig. 4, some sampling points still show negative values. Statistical analysis reveals that approximately 15% of the retained E-region observations are of negative values, and for the full electron density profile data, this proportion is much lower. Considering that when inverting Es layers, our criteria require ${\text{NmEs}}$ to be greater than the corresponding IRI-simulated values and that these negative values mostly appear below 90 km, their impact on our research results is negligible.

Fig. 4

Four electron density profiles are displayed to show the method for identifying the Es layers. In these panels, the black dots represent the original sampling points, while the blue lines represent smooth profiles plotted by interpolated points at 0.1 km intervals. The purple stars mark the electron density peaks within the 90–130 km altitude range. The yellow curves represent values fitted using the least squares method, and the pink curves illustrate the values derived from the IRI-2016 model. The criteria for judging Es layers require a peak factor $\ge 1.5$ and peak electron density that exceeds the corresponding IRI-simulated value

As shown in Fig. 5, for an RO EDP with an identified Es layer, the factors around the Es peak range from the minimum threshold of 1.5 to the maximum factor value. The average of these factors pinpoints the Es peak's midpoints. The most probable Es layer thickness is derived by comparing the height of the upper and lower midpoints. The lower left panel of Fig. 4 also specifies the two midpoints corresponding to event-3, which are used to calculate the thickness of the identified Es layer. The measured peak electron density of an Es layer, denoted as NmEs, is highlighted by purple stars in the two lower panels of Fig. 4. As mentioned earlier, NmEs includes the electron density from the surrounding E layer. To estimate the metallic ion density in an Es layer (NmμEs), following Haldoupis (2019), we subtract the corresponding IRI-simulated electron density from NmEs by using Eq. (6), which provides an unbiased measure of the Es layer’s intensity:

$$Nm\mu Es{ = }NmEs - NeE\left( {hEs} \right).$$

(6)

Fig. 5

A schematic diagram of the method for calculating the thickness of an Es layer. The orange wave peak represents the Es peak. The average value of the factors for all sampling points within the orange wave peak determines the middle two sampling points of this Es peak. The Es layer thickness is the difference in height between the middle two sampling points of the Es peak (h2–h1)

Here, NeE(hEs) represents the E-layer electron density from the IRI-2016 model. This value is calculated based on the time, longitude, latitude, and altitude of the Es layer occurrence.

5 Comparison between NmEs and ionosonde data

Utilizing reliable EDPs with scores of 0.6 or higher, we identified Es events and their parameters. To verify the accuracy of NmEs values, we compared these values with electron density values derived from the ionosonde measurements of fbEs. The ionosonde data were sourced from the Digital Ionogram Database (DIDBase) of the Global Ionospheric Radio Observatory (Reinisch and Galkin 2011) and the World Data Center for Ionosphere and Space Weather (WDC-ISW). Their websites are, respectively, https://giro.uml.edu/didbase/scaled.php and https://wdc.nict.go.jp/wdc-top/index.html. To ensure the reliability of the ionosonde data, for data from DIDBase, we selected only the files with confidence scores (CSs) $\ge$ 100 (automatically scaled data), and for data from WDC-ISW, we selected only manually scaled data. Comparisons are drawn between Es layers detected via RO EDPs and ionosonde measurements, using collocated data pairs. Our collocation criteria require the RO EDP-identified Es layer's latitude and longitude to be within 1 degree of the ionosonde station, and the time difference between the Es event from the RO EDP and ground observation to be less than 30 min. Moreover, for more meaningful comparison, the altitude difference between NmEs and fbEs must not exceed 5 km. The matched ionosonde stations and their respective number of observations that meet these criteria are depicted in Fig. 6.

Fig. 6

Geographical distribution of ionosonde stations and the corresponding data volume statistics

Figure 6 demonstrates that the selected ionosonde stations span the latitudinal range from ${70}^{\circ }$ S to ${70}^{\circ }$ N, aligning with the latitudinal coverage of the RO dataset. The total number of matched observations across all stations is 51. Considering the dataset employed by Niu et al. (2019a), the volume of ionosonde data matched in this study is slightly lower. This discrepancy is mainly attributed to the implementation of stricter temporal constraints (Niu et al. (2019a) employed a time difference threshold of one hour) and additional altitude restrictions, aimed at enhancing the reliability of comparative experiments. For an effective comparison with NmEs values, the fbEs values from collocated ionosonde measurements are converted to electron density values using the following formula (Reddy and Mukunda Rao 1968):

$${N}_{e}=1.24\times {10}^{4}{\left({\text{fbEs}}\right)}^{2}.$$

(7)

Here, fbEs is in MHz, ${N}_{e}$ is in electrons per cubic centimeter (el/cm³).

To quantitatively evaluate the discrepancies between NmEs values and fbEs-derived electron densities, we employed two statistical measures: the mean absolute percentage error (MAPE) and the root mean square error (RMSE). These are defined by the following formulas:

$$\text{MAPE}=\frac{1}{n}{\sum }_{i=1}^{n}\left|\frac{{x}_{i}-{y}_{i}}{{x}_{i}}\right|\times 100\%,$$

(8)

$$\text{RMSE}=\sqrt{\frac{1}{n}{\sum }_{i=1}^{n}{\left({x}_{i}-{y}_{i}\right)}^{2}.}$$

(9)

Here, ${x}_{i}$ represents the electron density derived from ith fbEs observation, while ${\text{y}}_{i}$ refers to the corresponding NmEs observation value.

Figure 7 depicts the correlation between NmEs values from RO EDPs and electron density computed using ionosonde-observed fbEs from 2006 to 2019. The Pearson correlation coefficient is 0.72, with a MAPE of 36.08% and a RMSE of $3.93\times {10}^{4 }\text{el}/{\text{cm}}^{3}$. Gooch et al. (2020) conducted a comparison on the Es layer intensities detected by ionosonde and those derived from RO data by using different methods. In their work, the correlation coefficients between ionosonde-observed Es layer intensities and RO-derived ones vary between 0.23 and 0.36, which are generally smaller than the one presented in Fig. 7, and the MAPEs of RO-based Es layer intensities derived by various methods range between 31 and 36%, which is consistent with our results. Additionally, most data points in Fig. 7 fall below the black dashed line, indicating that the NmEs values derived from RO EDPs are generally smaller than those computed using the ionosonde-observed fbEs values. Gooch et al. (2020) also noted that the RO-derived Es intensities by using the RO TEC with variable thickness method are generally smaller than those observed by ionosondes (as seen in the green triangles in their Fig. 8), and they pointed out that a key factor leading to this discrepancy is likely the different altitudes of the Es layers detected by RO and ionosonde methods, with RO observations showing significantly lower Es layer altitudes. Recognizing the methodological differences between RO and ionosonde observations, we extended our analysis to include a comparison with the RO S4 index, offering a more comprehensive assessment of the accuracy in detecting Es layers using EDPs.

Fig. 7

Comparison of NmEs derived from RO EDPs and the electron density derived from collocated ionosonde fbEs data spanning the years 2006–2019. The blue dots represent Es events selected based on matching criteria, and the black dashed line indicates a perfect relationship of y = x

Fig. 8

Scatter plot of NmEs versus matched S4max values during the period from 2006 to 2019. The least squares fitting of these data is depicted with a yellow line. The y-axis on the right shows the number of matched S4max values (red curve) and cumulative percentage (green curve), with 0.01 S4max value as the step size

6 Comparison between NmEs and S4 index

We compare NmEs values with the widely used RO S4 scintillation index. S4 index data are sourced from COSMIC-1 RO mission's Level 1b products (scnLv1 files), available on the UCAR CDAAC website. For brevity, we use only S4max index data. We conduct comparisons between NmEs values of Es layers and the S4max index using collocated RO file pairs. Initially, we match the fileStamps of EDP and S4 index files to ensure each EDP-S4 file pair is from the same RO event. Moreover, we maintain that the altitude discrepancy between NmEs and S4max does not exceed 0.5 km.

Figure 8 presents a scatter plot that illustrates the relationship between NmEs values from RO EDPs and corresponding RO S4max from 2006 to 2019. The analysis shows a linear correlation coefficient of 0.69 and a fitting line slope of 15.52. This correlation coefficient closely aligns with the findings of Tsai et al. (2018) on the connection between dNe and SDL1_max. Considering the thresholds set by Tsai et al. (2018), Arras and Wickert (2018), and Qiu et al. (2021), scatter points with an S4max below 0.2 are categorized as non-Es events. As a result, Es events identified via RO S4max constitute around 85.3% of those detected through RO EDPs, suggesting a potential misclassification rate of about 14.7% for Es events identified using EDPs (with S4max less than 0.2). This discrepancy is expected, given the methodological differences in Es layer detection. For example, various methodologies applied to the same type of observational data have yielded different occurrence rates for Es layers (Arras et al. 2008; Chu et al. 2014; Tsai et al. 2018). Therefore, the high 85.3% accuracy rate in identifying Es layers using EDPs underscores the effectiveness and reliability of EDPs in Es layer inversion.

7 Results

Our subsequent research primarily focuses on the characteristics of the Es layers in low and middle latitude regions (${70}^{\circ }$ S–${70}^{\circ }$ N). We organize the reliable EDPs dataset into four seasonal categories: MAM (March–April–May), JJA (June–July–August), SON (September–October–November), and DJF (December–January–February). Additionally, we present geographic distribution maps of the Es layers, incorporating geomagnetic latitude contours derived from the IGRF12 model.

Figure 9 depicts the geographical distribution of Es layer counts from 2006 to 2019. For each grid of ${5}^{\circ }\times {5}^{\circ }$, the number of Es events is determined by counting the events within that specific grid. The distribution of Es layers is strongly correlated with geomagnetic and geographic locations, exhibiting marked seasonal variations. Es events are more frequent in the northern and southern mid-latitude regions and less common near the geomagnetic equator. Peak Es activities occur in both mid-latitude areas during their respective summer seasons. In the Northern Hemisphere's mid-latitudes, grid counts of Es events typically range from 50 to 130. Notably, an abnormal region exists in the Americas (longitude ${70}^{\circ }$–${120}^{\circ }$ W), with fewer Es events compared to other areas within this latitude range. However, in the typical South Atlantic Anomaly area (Arras et al. 2008; Tsai et al. 2018), the occurrence of Es layers does not exhibit a significant decline compared to other regions at similar latitudes. This may be attributed to the uneven geographical distribution of COSMIC-1 RO observations. To reduce the influence of this distribution disparity on Es layers, we examined the occurrence rate of Es layers, as depicted in the subsequent Fig. 10.

Fig. 9

Seasonal variation in the geographical distribution of sporadic-E layer counts from 2006 to 2019 with a ${5}^{\circ }\times {5}^{\circ }$ latitude/longitude grid resolution

Fig. 10

Seasonal variation in the geographical distribution of the sporadic-E layer occurrence rates from 2006 to 2019, with a ${5}^{\circ }\times {5}^{\circ }$ latitude/longitude grid resolution

Figure 10 depicts the seasonal variation in the geographic distribution of Es ORs. To calculate Es ORs, we divide the count of Es events in each grid area by the number of RO EDPs used in there. In this and the subsequent experiments, geographic grid areas with fewer than three Es events are not considered, remaining blank in the panels. Figure 10 highlights the regions with anomalously low Es ORs values over North America and the South Atlantic. These lower Es ORs are linked to the wind shear theory (Whitehead 1961), largely due to the significantly weaker horizontal components of Earth’s magnetic field in these areas (Arras et al. 2008; Tsai et al. 2018; Luo et al. 2021). The other geographic and seasonal variations in Es ORs are similar to those observed in the Es layer counts. Our study records lower Es OR magnitudes compared to those in previous research, including Tsai et al. (2018) and Luo et al. (2021). This difference may arise from the data selection criteria in our study, which only includes EDPs spanning the E-region with a reliability score not less than 0.6. As a result, some EDPs influenced by Es layers but not covering the entire region or with lower reliability scores are excluded. This leads to a reduced count of Es layer events in our statistical analysis.

Figure 11 displays the seasonal variation in the geographic distribution of peak electron densities (NmEs) observed by COSMIC-1, calculated as the mean value of NmEs within each grid. In terms of spatiotemporal variation patterns, NmEs values show similarities to Es ORs, with both exhibiting a summer increase and winter decrease. Notable declines in NmEs values are also observed in North America and the South Atlantic regions. The NmEs values in mid-latitude areas predominantly range between $11\times {10}^{4}$ and $17\times {10}^{4}\text{el}/{\text{cm}}^{3}$ during summer, while in winter, they decrease to approximately $4\times {10}^{4}$ to $10\times {10}^{4}\text{el}/{\text{cm}}^{3}$. It is important to note that the values of NmEs might overestimate the Es layer intensities due to the influence of surrounding E-layer electron densities.

Fig. 11

Seasonal variation in the geographical distribution of NmEs values from 2006 to 2019, with a ${5}^{\circ }\times {5}^{\circ }$ latitude/longitude grid resolution

Figure 12 illustrates the seasonal average values of NmμEs within ${5}^{\circ }$ by ${5}^{\circ }$ latitude/longitude grids. It is observed that in the summer hemisphere's mid-latitude regions, the average NmμEs values are significantly higher than those in other regions and seasons, ranging between $5\times {10}^{4}$ and $8\times {10}^{4 }\text{el}/{\text{cm}}^{3}$. However, this range is noticeably 2–3 times lower than that of NmEs. The geographic distribution, seasonal variation, and amplitude variation range of NmμEs align with the results reported by Garcia-Fernandez and Tsuda (2006). They employed GPS phase observations from L1 and L2 frequencies, gathered by the CHAMP satellite at a 50-Hz sampling rate, to deduce electron density fluctuations (dNe(h)). Their findings indicate a summer maximum for dNe(h) in mid-latitude regions, with primary density values between $4\times {10}^{4}$ and $6\times {10}^{4 }\text{el}/{\text{cm}}^{3}$. The observations from rocket experiments also support our results. Yamamoto et al. (1998) analyzed the data from two sounding rockets launched during the SEEK experiment in Japan on August 26, 1996. They confirm that the Es layer peak electron densities predominantly range from $2.2\times {10}^{4}$ to $9.3\times {10}^{4}\text{ el}/{\text{cm}}^{3}$ at around 100 km altitude. Additionally, Roddy et al. (2004) examined high-resolution sounding rocket data collected by NASA on July 1, 2003. They found a peak electron density in intermediate layer (Es layer) to be approximately $4\times {10}^{4}el/{cm}^{3}$. These observational data align with our results in terms of the magnitude order and closely match in specific values.

Fig. 12

Seasonal variation in the geographical distribution of NmμEs values from 2006 to 2019, with a ${5}^{\circ }\times {5}^{\circ }$ latitude/longitude grid resolution

The seasonal variation in the geographic distribution of the gridded averages of Es layer thicknesses (not shown here) is less pronounced compared with those of Es ORs and densities. Figure 13 shows the density scatter plots of the thickness values across various magnetic latitudes during different seasons. The purple curve in each panel represents the number of Es events counted according to geomagnetic latitudes, while the black curve represents the cumulative percentage curve calculated based on the Es layer thicknesses. The cumulative percentage curves in the panels for different seasons all indicate that most Es layers have thicknesses between 0 and 3.0 km, and such Es layers account for more than 80% of the total Es events. This finding aligns with Whitehead (1989)'s estimates of Es thicknesses, which range from 0.6 to 2.0 km. As shown in Fig. 13, the thickness range of the Es layers is mainly 1.0–2.0 km, and further numerical analysis reveals that the most common thickness is approximately 1.4 km. Based on RO data, Bergsson and Syndergaard (2022) reported an average thickness of approximately 1.5 km, while Tsai et al. (2018) found the most frequent thickness to be about 1.2 km. Our results are basically consistent with these previous studies.

Fig. 13

Density scatter plots of the Es layer thicknesses across various magnetic latitudes during different seasons from 2006 to 2019. The magnetic latitude/thickness grid resolution is ${1}^{\circ }\times 0.1\text{ km}$. The purple curves represent Es event counts per ${1}^{\circ }$ magnetic latitude interval (the corresponding scale is shown on the top X-axis). The black curves indicate the cumulative percentage curves (the corresponding scale is displayed on the right Y-axis), with a statistical step of 0.1 km thickness interval

8 NmEs/NmμEs ratios

To further investigate the impact of the background E layer on Es intensity assessment, the ratio of NmEs over NmμEs is defined using Eq. (10) (Haldoupis 2019; Haldoupis et al. 2020):

$${\text{ratio }} = NmEs/Nm\mu Es.$$

(10)

Figure 14 shows the density scatter plots for the magnetic latitude distributions of NmEs/NmμEs ratios in daytime and nighttime of JJA and DJF seasons. Each grid filled with gray indicates that there are less than 5 Es events in that grid. As can be seen in Fig. 14, most ratios are larger than 1, demonstrating that NmEs values generally overestimate Es layer intensities. The right two panels of Fig. 14 show that during nighttime, the ratio values mainly range between 1.0 and 2.0, and the density peaks appear in the middle latitudes with the ratio values approaching 1, as presented by the grids with red color. The left two panels of Fig. 14 show that in daytime, the ratio values mainly vary between 1.0 and 4.0, with density peaks appearing in the middle latitudes around the ratio values of about 1.6. This significant day–night difference in the density distribution of ratio values indicates that NeE(hEs) has a more substantial impact on Es layer intensity during daytime than at night, which is also consistent with Haldoupis et al. (2020). However, the variation ranges of the ratio values shown in Fig. 14 are larger than those presented in Haldoupis et al. (2020), which should be mainly attributed to the inherent precision differences between RO and ionosonde observations. Nonetheless, the conclusions of this study are consistent with findings from previous literature in terms of overall trends.

Fig. 14

Density scatter plots of the ratios of NmEs to NmμEs across various magnetic latitudes in daytime (6:00–18:00 LT) and nighttime (0:00–6:00 LT; 18:00–24:00 LT) for JJA and DJF seasons from 2006 to 2019. The grid resolution for magnetic latitudes and ratios is ${1}^{\circ }\times 0.1$. The purple curves represent Es event counts per ${1}^{\circ }$ magnetic latitude interval (the corresponding scale is shown on the top X-axis). The black curves indicate the cumulative percentage curves (the corresponding scale is displayed on the right Y-axis), with a statistical step of 0.1 in the ratio interval

Figure 15 further shows the density scatter plots for the altitude distributions of NmEs/NmμEs ratios in daytime and nighttime of the summer hemispheres. The purple curves indicate that the peak numbers of Es layers occur at the altitudes of about 100–102 km. In the summer hemispheres, the frequencies of larger ratio values are in general higher in daytime than those at night. Besides, during the day, the ratio values also show a clear altitude dependence: the lower the altitudes, the closer the ratios approach 1. However, this dependence was not evident at night. Just like the diurnal variation in the ratio values, this altitude dependence can also be explained by the variation of NeE(hEs) with altitudes. The reason is that when solar radiation passes through the ionosphere during the day, its energy is gradually absorbed by atmospheric molecules. This results in lower solar radiation energy at lower altitudes, which in turn slows down the rate of molecular ionization in the area. Under the recombination of ions and electrons, the environmental electron density in low-altitude areas decreases (Kelly, 2009), so the impact on the Es layer intensities decreases and the ratio values decrease.

Fig. 15

Density scatter plots of the ratios of NmEs to NmμEs across various altitudes in daytime (6:00–18:00 LT) and nighttime (0:00–6:00 LT; 18:00–24:00 LT) in the summer hemispheres from 2006 to 2019. The grid resolution for altitudes and ratios is $1 \text{km}\times 0.1$. The purple curves represent Es event counts per 1 km altitude interval (the corresponding scale is shown on the top X-axis). The black curves indicate the cumulative percentage curves (the corresponding scale is displayed on the right Y-axis), with a statistical step of 0.1 in the ratio interval

9 Conclusions

We present an improved method for detecting Es layers through the analysis of ionospheric E-region electron density profiles (E-region EDPs). These EDPs, sourced from COSMIC-1 RO igaPrf files, cover the period from 2006 to 2019. For reliability assessment, we utilize the weighted normalized root mean square error (WNRMSE) and correlation coefficients, comparing the EDPs with simulated values from the IRI-2016 model. The RO EDPs with reliability scores of 0.6 or higher are utilized for detecting Es layers. The main findings are summarized as follows:

• 1. The accuracy of the Es layer inversion is validated by comparing NmEs with ionosonde measurements (fbEs) and the COSMIC-1 RO S4max index under comparable conditions. A strong linear relationship is evident between NmEs and fbEs-derived electron density, indicated by a correlation coefficient of 0.72. Additionally, a mean absolute percentage error (MAPE) of 36.08% is observed, with a root mean square error (RMSE) of $3.93\times {10}^{4 }\text{el}/{\text{cm}}^{3}$. When compared to the S4max inversion results, Es layer detection exhibits an accuracy of 85.3%. Given the inherent differences in the methods used for Es layer inversion, the use of EDPs for detecting the Es layers is considered reliable.

• 2. Our comprehensive study on Es layers focuses on their occurrence rates (Es ORs), intensity (NmμEs), and thickness. We find that Es layers predominantly appear in mid-latitude regions during summer. The summer average intensity of Es layers in these regions ranges from $5\times {10}^{4}\text{ to }8\times {10}^{4} \, {\text{el}}/{\text{c}}{\text{m}}^{3}$. This finding aligns with the research of Garcia-Fernandez and Tsuda (2006) and rocket observation results. Besides, our statistical analysis of Es layer thicknesses reveals that they are usually smaller than 3 km, with a most common thickness of 1.4 km.

• 3. We assess the impact of E-layer electron density (NeE(hEs)) on Es layer intensity estimations using the NmEs/NmμEs ratios. Observations suggest that the existence of NeE(hEs) may result in the overestimation of Es layer intensity. This effect leads to daytime NmEs being 1–4 times higher than NmμEs, with a decrease at night to only 1–2 times. Additionally, the study further revealed that during the day, the influence of NeE(hEs) on the Es layer intensity shows a clear altitude dependence. Specifically, when the altitude decreases, the NmEs/NmμEs ratios gradually approach 1, indicating that in areas with lower altitudes, the influence of NeE(hEs) on the Es layer intensity is relatively weakened.

• 4. The use of COSMIC-1 RO igaPrf EDPs for Es layer inversion offers distinct benefits and challenges. This method provides electron density values for mid-latitude Es layers and enables direct thickness calculations. However, the initial E-region EDPs exhibit some instability, with only 42.7% of all E-region EDPs meeting reliability criteria. Due to this reduced data volume, this study has not yet investigated diurnal variations in the Es layers. Additionally, the data selection criteria applied in the present study may results in that some profiles influenced by the Es layers but not meeting our data selection criteria were inevitably excluded, potentially contributing to our Es ORs being lower than those reported in some previous studies based on other types of RO datasets.