The E region of the ionosphere plays an important role in ionospheric conductivities that impact ground-based magnetometer observations , atmospheric energy input and balance , and High Frequency (HF) radio propagation . Therefore, a proper understanding of global E region morphology can provide insight into both scientific and practical applications, especially through the use and development of E region models.

Critical frequencies of the E region (foE; or corresponding peak electron density NmE) have been studied for many years, revealing a relationship with the solar zenith angle , season , sunspot number , and Sun-Earth distance . Global collections of ionosondes have provided insight into foE variation over time, such that empirical relationships could be developed (e.g., ). Similarly, rocket and incoherent scatter radar data have been used to calculate empirical NmE trends . As the E region is photochemistry dominated and driven primarily by extreme ultraviolet (EUV) flux with wavelengths below 150 Å , chemistry models have been created , providing insight into difficult-to-measure densities (such as [NO]) and reaction rates and coefficients.

Models of the peak electron density altitude of the E region, hmE, have also been developed . These studies have shown that hmE remains nearly constant around local noon at lower altitudes, with increases in altitude near sunrise and sunset. The general behavior of hmE can be captured by Chapman theory , providing a linear relationship with the natural log of the secant of the solar zenith angle. derived a modified Chapman theory dependence for hmE taking into account season, latitude, solar flux, solar zenith angle and local time, resulting in hmE values between 105 and 120 km that agree well with ionosonde observations from Auckland, New Zealand.

A Chapman-layer E region can be approximated as a quasi-parabola , requiring a peak altitude, peak density, and half-thickness (scale height) to describe the bottomside shape. These parameters can be calculated using virtual height measurements from ionosondes , making ionosondes a powerful tool for extracting E region electron density profiles (EDPs). For this reason, long-term ionosonde observations have been used as the backbone of global bottomside E region models such as the empirical International Reference Ionosphere (IRI; . While Incoherent Scatter Radar (ISR) observations contribute to IRI's estimates for the E-F valley, foE and hmE are mainly driven by ionosonde observations . Recently, the core framework of IRI has been implemented in Python instead of the historical Fortran approach in the new PyIRI , allowing for more rapid execution of global ionospheric profiles. Similar to the core of the IRI model, PyIRI uses the global Consultative Committee on International Radio (CCIR) and the International Union of Radio Science (URSI) coefficients for foF2 and the HF propagation parameter M(3000)F2 (Maximum Usable Frequency for a distance of 3000 km normalized to foF2) that can be used to calculate hmF2 . PyIRI currently implements the standard options from IRI while also using certain features of NeQuick for the top-side and E region such that the overall model is a combination of IRI and NeQuick. This results in nearly identical results between PyIRI and IRI-2020 for certain parameters such as hmF2, while producing different EDP shapes due to the NeQuick features and differences in EDP construction . Although the focus of the present study is on the E region, IRI provides an empirical estimate of the entire ionosphere (all ionospheric altitudes), resulting a quick and easy-to-run model widely used by the ionospheric community.

With recent improvements in Global Navigation Satellite System (GNSS) Radio Occultation (RO) techniques for extracting D and E region electron densities , global E region observations are now available in regions that were previously unobtainable by ionosondes or ISR . GNSS-RO provides horizontally integrated observations of the ionosphere and atmosphere, using signals of opportunity from GNSS and a Low Earth Orbit (LEO) satellite to receive the signals , resulting in a large and globally distributed observational dataset for the ionosphere (e.g., ). These global GNSS-RO observations have been used to develop a modern E region model, E region Prompt Radio Occultation Based Electron Density (E-PROBED; ). The model was developed using Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1) observations of the E region from 2007–2016 and is driven by Solar Zenith Angle (SZA), season, and F10.7 with an additional non-SZA component that is a function of latitude, local time, season, and F10.7 . Time series of NmE, hmE, and scale-height for each latitude-local time bin were fit to Fourier coefficients up to the 10th harmonic, providing a lookup table for each bin that is called within E-PROBED. GNSS-RO derived EDPs used to drive E-PROBED were estimated using a bottom-up approach that limits F region contributions through a weighting function with minimal contributions from higher altitudes, unlike the standard Abel transform typically used for RO inversion . Ultimately, this global GNSS-RO dataset provides a novel method for estimating bottomside EDPs, with E-PROBED encompassing the observations into an empirical model that can predict global E region EDPs for altitudes between 90–120 km.

While the truly global spread of GNSS-RO observations provides great promise for remote sensing of the upper atmosphere, the integrated nature of the measurements motivates the need for additional comparison against more direct observations such as those implemented by ionosondes. The same argument holds for models derived from GNSS-RO (E-PROBED) versus ionosonde (PyIRI) observations of the E region. A recent study by has provided a framework for this comparison between EDPs derived from GNSS-RO, ionosondes, and models. In the present study, we implement many of the same approaches to compare modeled E regions from E-PROBED and PyIRI to ionosonde observations used as the “ground-truth” validating dataset. This effort aims to provide insight into model performance as well as the solar cycle, seasonal, and diurnal morphology of the E region for several ionosonde sites spanning low-, mid-, and high-latitudes.

Three Digisonde sites were selected as the basis for this comparison: Fortaleza, Brazil (URSI code FZA0M, 3.9° S, 321.6° E, -21.5° inclination), El Arenosillo, Spain (EA036, 37.1° N, 353.3° E, 50.6° inclination), and Gakona, USA (GA762, 62.4° N, 215.0° E, 75.5° inclination). These three sites span low-, mid-, and high-latitudes, providing a comparison over a variety of ionospheric conditions. Ionosonde virtual height observations, foE, and hmE estimates were obtained from the Digital Ionogram Database . Virtual heights were obtained using SAOExplorer version 3.6.1 while the foE and hmE estimates were downloaded directly from DIDBASE. The virtual height observations have a frequency resolution of approximately 25 kHz and Digisondes use a standard temporal resolution of one ionogram every 15 min. However, the temporal resolution can be variable, sometimes increasing up to 5 min per ionogram. In addition, there are several periods with outages at each site, which can last anywhere from days to years. It should also be noted that the minimum foE observations from ionosondes are constrained by the minimum transmit frequency and sensitivity, such that nighttime foE values below ∼1.5 MHz are generally not measured by ionosondes. Therefore, the comparison performed here does not include nighttime observations or model estimates.

To provide a long-term comparison, automatically-scaled ionograms using the Automatic Real-Time Ionogram Scaler with True Height calculation version 5 (ARTIST-5; ) were used for foE and hmE estimates. The start dates for implementing ARTIST-5 vary from site to site, with El Arenosillo implementing in December 2008, Fortaleza in November 2014, and Gakona in May 2007. From this, the foE and hmE comparison for each site begins on the date of ARTIST-5 implementation and continues through 2024. Within each of these periods, a collection of manually-scaled ionograms are also available, with the largest density for EA036 in 2009.

Although auto-scaled ARTIST-5 ionograms are known to differ from manually-scaled profiles (e.g., ), the use of auto-scaled ionograms allows for a prolonged comparison period to analyze long-term trends. In an attempt to remove poor quality ionograms from the comparison, ARTIST confidence scores were required to be above 90 %. While it is not entirely clear how these confidence scores map to an uncertainty in electron density as a function of altitude, the 90 % confidence threshold requires a series of quality control criteria to be satisfied such that noisy or problematic ionograms are removed . Furthermore, we implemented additional criteria to be satisfied as an expanded quality control procedure: the foE was required to be above the minimum transmitted frequency, fmin, profiles with sporadic-E (foEs) observations were removed, hmE values were required to be above 90 km, and hmE estimates of exactly 110 km were removed. The removal of 110 km hmE values was implemented because of a large number of ionograms that defaulted to this altitude, likely following climatological estimates and not derived entirely from the observations. This 110 km hmE altitude will be discussed in more detail in Sects.  and .

Geomagnetically quiet conditions were also enforced for the comparison by constraining Kp ≤3, with Kp values obtained from NASA's OMNIWeb . This ensures that differences in E region observations and model predictions are not reliant on the model's ability to predict variations caused by geomagnetic activity. Both E-PROBED and PyIRI were run for each ionogram time satisfying the criteria outlined above. In total, this results in 19 727 foE and hmE observations for EA036 (including 896 manually-scaled ionograms), 54 036 for FZA0M, and 3837 for GA762.

For the models, E-PROBED version 1.0 was used to estimate E region EDPs using longitude, latitude, altitude range (90–130 km with 0.25 km resolution), date, and time of day as input. The foE and hmE estimates were calculated from the EDPs using Scipy's find_peaks function , that performed well on the smooth E-PROBED profiles with a single E region peak. PyIRI profiles were calculated using version 0.0.2 with an altitude range of 90–130 km and a resolution of 0.25 km. The PyIRI inputs are longitude, latitude, date, time of day, F10.7, altitude range, and an option for NmF2 calculations, ccir_or_ursi, which was set to use the CCIR coefficients. The foE and hmE values were output directly from PyIRI.

Although foE can be observed directly from virtual height observations as an E region cusp (assuming foE is outside of a restricted transmission band), hmE estimates are calculated through a quasi-parabolic fit to the virtual height data (e.g., ), which results in additional uncertainty for the hmE estimates. To account for this additional uncertainty in the altitude estimates, a comparison to directly measured ionogram virtual heights is performed on a subset of the data. Virtual height observations contain information on the shape and magnitude of EDPs through the group index of refraction , which provides a more direct comparison against ionosonde observations than comparing against inverted EDPs that require a series of assumptions on the profile shape, etc. . The E-PROBED and PyIRI EDPs were converted to virtual heights through the use of a High Frequency (HF) ray tracer. Specifically, the EPDs were input into Another Ionospheric Ray Tracer (AIRTracer; a model developed by Eugene V. Dao at the Air Force Research Laboratory) to calculate virtual heights for ordinary-mode rays. AIRTracer uses the Jones-Stephenson formulation with the Booker quartic and no collisions, and has been rewritten in the Julia Programming Language to decrease computation time. For each subset of ionograms used for the virtual height comparison, a group path is calculated for each transmit frequency of the ionogram virtual height data (roughly 25 kHz resolution) using the E-PROBED and PyIRI EDPs. The virtual height is then taken as half of the group path. Due to the additional processing time required to calculate the virtual heights of E-PROBED and PyIRI, the observation subset was limited to January-March 2009 for EA036 (total of 618 profiles), August 2019 for FZA0M (711 profiles), and May 2008 to January 2009 for Gakona (515 profiles). These periods were selected when the data density was large for the site of interest, and the period selected for EA036 includes the manually-scaled ionograms. A total of at least 500 profiles was desired for each site, which resulted in variable time spans due to differences in ionogram cadence and quality (i.e., lack of ionospheric disturbances, etc.).

The comparison results are separated by the ionosonde site, and the combined trends will be discussed in Sect. . For each site, the trends are analyzed by year (solar cycle), day of year (seasonal), and solar local time (diurnal), with seasonal and diurnal results displayed in Appendix . Then, the modeled virtual heights predicted by E-PROBED and PyIRI are compared with ionosonde observations for a subset of the ionograms.

Overall, both E-PROBED and PyIRI show reasonable agreement with the ionosonde observations spanning low-, mid-, and high-latitudes; the combined statistics are displayed in Table . Between foE and hmE, both models show better agreement with foE. PyIRI shows close foE agreement with ionosonde observations producing MAE values between 0.1–0.2 MHz. E-PROBED's foE MAE values are slightly larger (0.4–0.5 MHz), but still within a reasonable range of the ionosonde observations. For comparison, an foE uncertainty of ± 0.3 MHz is estimated by for ionogram inversion.

PyIRI calculates foE in a manner similar to NeQuick , somewhat different from IRI, with the magnitude of foE as a function of the effective SZA, a seasonal parameter, and the F10.7 solar radio flux . This NeQuick foE relationship was adopted from , which used a photochemistry-based model in comparison against ionosonde-based IRI and results from . In contrast, E-PROBED is derived from COSMIC-1 radio occultation observations and is driven by SZA, season, and F10.7, with an additional non-SZA component that is a function of latitude, local time, season, and F10.7 . Although the foE (NmE) Fourier coefficient calculations from E-PROBED are more complicated than the analytical PyIRI approach, they also provide more variability over time and latitude (see Fig. 9 of ).

It should be noted that the largest MRAE for E-PROBED foE predictions occurred near dusk when large ionospheric tilts are present that impact the HF ray-paths used to create ionograms . These ionospheric tilts result in off-zenith observations, inducing additional errors into the ionogram inversion process that assumes vertical propagation . The elevated MRAE for Gakona in winter may also be influenced by this phenomenon, where the short period of sunlight can be considered dawn/dusk instead of daytime. PyIRI's close relationship with historical ionosonde data likely incorporates the impact of the ionospheric tilts on the dawn/dusk ionograms, as observed for the low dawn/dusk MRAE shown here. However, as outlined by , the largest zenith variations are observed during sunrise, whereas the variation during sunset is minimal, suggesting that ionospheric tilt-induced uncertainties in ionogram observations are probably not the cause of larger E-PROBED errors near dusk. Ionospheric inhomogeneities are known to cause errors in radio occultation derived EDP estimates, with high inclination (cross-latitude) orbits more susceptible to impacts than low inclination (cross-longitude) orbits . As E-PROBED was developed using observations from the high inclination orbits of COSMIC-1, the EDP estimates are more prone to these horizontal density gradients in the ionosphere. During dusk, with the large ionospheric tilts from the solar terminator and other features such as the Appleton Anomaly and prereversal enhancement surrounding the geomagnetic equator , large horizontal density gradients are certainly present in the ionosphere. These horizontal gradients impact RO derived EDP estimates, increasing uncertainties and potentially contributing to foE overestimation by E-PROBED during dusk.

In addition to the various large-scale gradients outlined above, low-, mid-, and high-latitudes are all prone to ionospheric irregularities that affect both ionosonde and GNSS-RO observations. From low-latitude disturbances caused by equatorial electrojet irregularities and equatorial plasma bubbles to mid-latitude sporadic-E and high-latitude auroral electron precipitation , these irregularities induce additional uncertainties into the measurements used as ground-truth and as drivers for PyIRI and E-PROBED. Due to the drastically different approaches used to probe the ionosphere, a differential contamination of irregularities is manifest in the ionosonde and GNSS-RO datasets; the integrated nature of GNSS-RO increases the likelihood of encountering ionospheric irregularities while traversing large distances across the ionosphere while ionosondes are local observations with fairly narrow fields of view for vertical ionograms (e.g., ). In fact, the elevated electron densities predicted by E-PROBED near dusk during summer align well with the expected formation of sporadic-E, which peaks near summertime dusk . The phase-based EDP estimates from GNSS-RO used to drive E-PROBED are unable to distinguish between background and metallic-ion densities, which likely results in peak E region electron densities (NmE) greater than the background NmE measured by ionosondes. If the overestimation of dusk foE by E-PROBED is primarily driven by ion density enhancements from sporadic-E, then the elevated densities may be helpful for certain applications such as estimating ionospheric conductivities, where the sporadic-E contribution will enhance conductivity when present . While quantifying these contributions and uncertainties is difficult and worthy of individual studies, we simply note here that uncertainties caused by ionospheric irregularities are present in the datasets and will vary for each of the ionosonde sites.

For hmE, the PyIRI constant hmE estimate of 110 km results in lower MAE values than the variable hmE predictions from E-PROBED. However, the resulting R2 and Spearman rank-order correlation coefficients (ρ) for PyIRI's hmE predictions are essentially zero, while ρ for E-PROBED hmE ranges from 0.11-0.25. The constant daytime hmE of 110 km in PyIRI originates from IRI's constant value of 105 km that was changed to “110 km based on input from ionosonde and ISR observations” . As suggested by , these “reflect the uncertainty caused by a lack of good observational data,” where good ionograms before the year 2000 could only be scaled with a virtual height accuracy of 2–3 km. Even the modern Digisonde 4D has a range resolution of 2.5 km . However, as developed by from ISR observations and from ionosondes, time-varying hmE models are currently available showing hmE variations between 105–120 km, which may be beneficial for implementation in IRI/PyIRI.

The large difference between auto-scaled and manually-scaled hmE estimates as observed in Fig.  must be taken into account to fully understand the uncertainties involved with auto-scaled ionogram parameters. The manually-scaled hmE estimates over EA036 are nearly 15 km above the auto-scaled values for the same conditions, closely matching the E-PROBED hmE estimates. ARTIST-5 auto-scaling uncertainties have been analyzed in detail by for the Dourbes, Belgium Digisonde during 2011–2017, resulting in foE error bounds (auto-scaled value minus manually-scaled value) of [-0.30,0.80] MHz and minimum virtual height of the E region, h′E, error bounds of [-6,6] km. While the modeled foE values fall within the auto-scaled ionogram uncertainties for foE, the auto-scaled h′E uncertainties are rather low compared to the models' hmE MAE between 6–15 km. However, the auto-scaled h′E error bounds during low solar activity show a large underestimation bias for the auto-scaled estimates ranging from [-15.0,2.5] km . The -15 km error bound matches the 15 km hmE underestimation observed during the 2009 solar minimum over EA036, indicating that the large errors in E-PROBED hmE estimates during solar minimum may simply be an artifact of auto-scaled errors. As the auto-scaled error bounds are reduced during solar maximum, the E-PROBED hmE estimates are overestimated during these times. The general trend of underestimated peak height altitudes from ARTIST-5 auto-scaled ionograms was also observed for hmF2 when compared against GNSS-RO and ISR estimates , and the hmE differences between auto- and manual-scaled ionograms observed in Figs. – suggest that perhaps an offset could be calculated to correct the auto-scaled estimates. However, this offset would likely depend on several factors such as solar cycle and ionosonde site (hardware, climatology, etc.), requiring a significant effort to obtain appropriate correction factors. Ideally, a future study with a larger collection of manually-scaled ionograms spanning several years could be used to reanalyze the models' hmE predictions and remove the inconsistencies stemming from auto-scaling.

It must also be noted that hmE is dependent on a parabolic fit to the E region virtual height observations , which means that the scaling errors for h′E and errors in hmE are not expected to be one-to-one. However, differences in the starting altitude of virtual height observations will certainly impact the hmE estimates, and the differences between manually-scaled and auto-scaled hmE observations align well with the expected errors in h′E. An additional uncertainty/error within ionogram-derived hmE estimates is caused by the assumed parabolic layer shape for the E region that approaches a zero plasma frequency at the bottom of the E region rather than smoothly transition to the nonzero D region densities. As discussed in detail in , the lack of a D to E region transition during ARTIST-5 ionogram inversion along with a required parabolic profile fit (that can introduce exaggerated dz/dfp near foE) may result in a small bias for the bottom of the parabolic layer on the order of a few kilometers.

Compared with previous comparisons of E region models with ionosonde observations, the results generally align with the present study. found similar seasonal trends with the El Arenosillo Digisonde throughout 1995. They also found relatively close agreement with IRI's foE estimates and ionosonde observations, but noted that a chemistry-based model could reproduce the hmE variations not captured by IRI. The foE and hmE model developed by was able to reduce hmE errors to less than 5 km and foE errors below 0.1 MHz when compared to manually-scaled ionograms from Auckland, New Zealand, which is a significant reduction from the hmE errors observed here for E-PROBED and PyIRI. found that IRI overestimated foE over Wuhan, China, especially between May and September. developed a photochemistry-based NmE model that showed reasonable agreement with an ionosonde at Boulder, Colorado for low solar activity, but required a factor of 2 increase in the 3.2–7.0 nm flux from EUVAC to match observations during high solar activity. A comparison of IRI foE predictions with an ionosonde at Chumphon Station, Thailand, found the largest differences during sunrise and sunset, but very low overall errors . also found a slight overprediction by IRI compared to manually-scaled ionograms from the Nicosia, Cyprus Digisonde. For hmE, they observed similar diurnal and seasonal trends, although their manually-scaled ionograms provided hmE values below IRI's constant value of 110 km. Further, they conclude that large differences between IRI and the ionosonde observations may be due to non-Chapman like behavior of the E layer, which was also noted by . These results are consistent with the auto-scaled ionograms shown here, although our manually-scaled ionograms from EA036 show elevated hmE values above 110 km.

In contrast to foE and hmE estimates from ionogram inversions, virtual heights are directly measured by ionosondes, making them a useful tool for model validation. The virtual height (h′) for a particular transmit frequency (f) is defined as the integral of the group index of refraction as a function of altitude, which may also be represented as the group index (μ′) as a function of frequency times the gradient of the real-height with respect to frequency: 1h′(f)=∫0fμ′(f,fp)dzdfpdfp,2μ′=1-fp2f2-1/2, where fp is the plasma frequency . Equation () is a simplified form of the group index of refraction for an unmagnetized, collisionless plasma, and is shown here instead of the full form for an O-mode to show the basic relationship with respect to the plasma frequency. This dependence on fp and dz/dfp provides a method for analyzing modeled E region shapes and gradients that is free from uncertainties produced by profile shape assumptions used during ionogram inversion. However, due to the integrated nature of the virtual heights, it is possible to produce the same virtual heights from various EDPs, meaning that virtual height agreement does not necessarily indicate agreement on profile shapes overall. Although a direct comparison with ionosonde-derived EDPs may seem like a more straightforward approach, the various assumptions required for ionogram inversion result in a final product that is no longer a direct measurement (see the discussion in ).

For the sites analyzed here, both PyIRI and E-PROBED showed reasonable agreement with the measured virtual heights with MAE ranging from 5–7 km for E-PROBED and 3–7 km for PyIRI (Table ). Although similar performance for both models may appear to indicate similar profiles that agree with ionosonde observations, the differences in predicted foE and hmE prove that this is not the case. Even with differing EDPs, the altitude integrals of the group indices derived from the EDPs result in similar virtual heights that generally agree with ionosonde observations. Although, a bias exists for each site: the models tend to underestimate the virtual heights for EA036, while the models tend to overestimate the virtual heights for FZA0M and GA762. Since the EA036 period of comparison for virtual heights was January–March 2009 (solar minimum) and was mostly composed of manually-scaled ionograms while FZA0M and GA762 consisted of auto-scaled ionograms, the change in bias from underestimation to overestimation is likely an artifact of ARTIST-5 autoscaled uncertainties for h′E . Even here, where we assume that the virtual heights are direct measurements to be used as ground-truth, an uncertainty exists from auto-scaling that must be considered when interpreting the accuracy of the modeled virtual heights.

A comparison of E region predictions from E-PROBED, PyIRI and ionosondes was performed for three sites: mid-latitude El Arenosillo, Spain (EA036), low-latitude Fortaleza, Brazil (FZA0M), and high-latitude Gakona, Alaska (GA762). Manually-scaled or auto-scaled ionograms using ARTIST-5 were used as the ground-truth for foE and hmE estimates, and both models were run for each ionogram time spanning from 2009–2024 for EA036 and GA762, and 2015–2024 for FZA0M. Additionally, a subset of ionograms were used to compare against modeled virtual heights calculated from the models using a numerical ray tracer.

The key results of the comparison are listed below:

Overall, both E-PROBED and PyIRI showed reasonable agreement with the ionosonde observations, properly capturing the foE solar cycle, seasonal, and diurnal trends.