# Validation of the IRI-2020 topside ionosphere options through in-situ electron density observations by low-Earth-orbit satellites

Alessio Pignalberi<sup>a,*</sup>, Dieter Bilitza<sup>b</sup>, Pierdavide Coïsson<sup>c</sup>, Haris Haralambous<sup>d,e</sup>, Bruno Nava<sup>f</sup>, Michael Pezzopane<sup>a</sup>, Fabricio Prol<sup>g</sup>, Artem Smirnov<sup>h,i</sup>, David R. Themens<sup>j,k</sup>, Chao Xiong<sup>l</sup>

Received 29 March 2024; received in revised form 21 May 2024; accepted 24 May 2024

Available online 28 May 2024

## Abstract

The topside ionosphere extends from the F2-layer peak, where the electron density reaches its absolute maximum in the ionosphere, to the overlying plasmasphere and magnetosphere. In the topside ionosphere, the electron density decreases with height with a vertical variation rate strongly dependent on height itself. The last version of the *International Reference Ionosphere* (IRI) model, i.e., IRI-2020, describes this complex behavior through four topside options based on different sub-models (i.e., options) developed from the 1970s to the present. All these options have in common the F2-layer peak as an anchor point, while they differ in their topside electron density profile and/or plasma effective scale height formulations. In this work, we perform a validation of the accuracy of the four IRI-2020 topside options based on the comparison against in-situ electron density observations by *Gravity Recovery and Climate Experiment (GRACE)*, *Ionospheric Connection Explorer (ICON)*, and *Defense Meteorological Satellite Program (DMSP)* F15 low-Earth-orbit satellites. Datasets used in this study encompass observations recorded from 1999 to 2022, covering different diurnal, seasonal, and solar activity conditions, on a global basis and for the height range 400–850 km above the ground. The nearly two solar cycles dataset facilitated the evaluation of IRI-2020 topside options ability to reproduce the spatial and time variations of the topside ionosphere for different solar activity conditions. The weaknesses and strengths of each IRI-2020 topside option are highlighted and discussed, and suggestions on how to improve the modeling of the challenging topside ionosphere region within the IRI model are provided for future reference.

© 2024 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

**Keywords:** Topside ionosphere modeling; International Reference Ionosphere (IRI) model; In-situ electron density observations; Low-Earth-Orbit satellites

<footnote><sup>a</sup> Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy</footnote>

<footnote><sup>b</sup> Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA</footnote>

<footnote><sup>c</sup> Université Paris Cité, Institut de Physique du Globe de Paris, CNRS, 75005 Paris, France</footnote>

<footnote><sup>d</sup> Department of Electrical Engineering, Computer Engineering and Informatics, School of Engineering, Frederick University, Nicosia 1036, Cyprus</footnote>

<footnote><sup>e</sup> Frederick Research Center, Nicosia 1036, Cyprus</footnote>

<footnote><sup>f</sup> The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy</footnote>

<footnote><sup>g</sup> Department of Navigation and Positioning, Finnish Geospatial Research Institute (FGI), National Land Survey of Finland (NLS), Vuorimiehentie 5, 02150 Espoo, Finland</footnote>

<footnote><sup>h</sup> Helmholtz Centre Potsdam - GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany</footnote>

<footnote><sup>i</sup> Ludwig Maximilian University of Munich, Theresienstr. 41, 80333 Munich, Germany</footnote>

<footnote><sup>j</sup> Space Environment and Radio Engineering Group (SERENE), School of Engineering, University of Birmingham, B15 2TT Birmingham, UK</footnote>

<footnote><sup>k</sup> Department of Physics, University of New Brunswick, 8 Bailey Drive, PO Box 4440, Fredericton, NB E3B 5A3, Canada</footnote>

<footnote><sup>l</sup> Department of Space Physics, Electronic Information School, Wuhan University, Wuhan 430072, China</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: alessio.pignalberi@ingv.it (A. Pignalberi).</footnote>
# 1. Introduction

The topside ionosphere is the ionized region of the upper atmosphere mainly extending from the F2-layer electron density peak to the overlying plasmasphere and magnetosphere (Rishbeth and Garriott, 1969; Ratcliffe, 1972). Historically, the upper transition height (UTH), that is the height where the percentage of $O^+$ ions is equal to the percentage of light $H^+$ and $He^+$ ions, is considered the upper limit of the topside ionosphere (Titheridge, 1976). However, both the F2-layer peak altitude ($hmF2$) and the UTH show large variations with space, time, and solar activity level, thus making the altitudinal extension of the topside region highly variable with time. For instance, the UTH ranges from about 500 km at night during low solar activity, to about 1,600 km at daytime for high solar activity (Vaishnav et al., 2021). As a result, the topside region encapsulates most of the ionospheric total electron content (TEC).

The topside is a highly dynamic region generally characterized by a decrease of the plasma density with altitude, driven by the plasma ambipolar diffusion along geomagnetic field lines (Bauer, 1969; Pignalberi et al., 2020a). The rate of the plasma density decrease is variable with altitude due to variations in both physical and chemical plasma parameters. Indeed, in the topside ionosphere, the chemical composition changes from a region dominated by $O^+$ ions at the F2-layer peak, to a region dominated by $H^+$ ions in the plasmasphere. In the same domain, the plasma temperature increases with altitude, thus modifying the plasma thermal diffusion rate (Banks, 1969; Schunk and Nagy, 1978). The combination of these two chemical and physical phenomena drives most of the altitudinal variation of the plasma vertical scale height and, as a result, the variation of plasma density in the topside ionosphere (Bauer, 1969; Liu et al., 2007a, Liu et al., 2007b; Pignalberi et al., 2020a).

The complexity of the interplay between these physical and chemical phenomena, including the highly-variable altitudinal extension of this region, deems the modeling of the topside ionosphere plasma density profile a challenging task, also augmented by the historical scarcity of plasma observations when compared to the bottomside ionosphere. Indeed, the topside is hidden to the widely spread ground-based ionosondes, and observations of the plasma require more sophisticated and expensive techniques like topside sounder satellites, incoherent scatter radars, in-situ measurements by low-Earth-orbit (LEO) satellites, and radio occultation of Global Navigation Satellite System (GNSS) signals (Hunsucker, 1991). Thanks to the ever-increasing number of LEO and classic GNSS satellites, in recent years the ever-growing availability of plasma observations in the topside has opened the avenue for the development and implementation of several topside models based on different data sources and modeling techniques (Stankov et al., 2003; Kutiev et al., 2006; Stankov and Jakowski, 2006; Reinisch et al., 2007; Kutiev and

Marinov, 2007; Tulasi Ram et al., 2009; Nsumei et al., 2012; Wang et al., 2015; Zhu et al., 2015; Olivares-Pulido et al., 2016; Wu et al., 2016; Hernández-Pajares et al., 2017; Pignalberi et al., 2018; Prol et al., 2018, 2019, 2022; Themens et al., 2018; Pezzopane and Pignalberi, 2019; Singh et al., 2021; Pignalberi et al., 2023; Smirnov et al., 2023).

The need for a reliable and accurate prediction of the topside ionospheric plasma behavior is necessary not only for scientific purposes but, more importantly, for LEO satellite construction and design, as the topside ionosphere is the environment in which these satellites fly. Moreover, since the topside ionosphere encapsulates a large fraction of TEC, it imposes the largest delay effect on GNSS signals traveling through the ionosphere (Hoque and Jakowski, 2012). The correction for the ionospheric range delay in GNSS signals is therefore of utmost importance for applications based on single-frequency GNSS signals; as provided by the Global Positioning System (GPS) with the Klobuchar model (Klobuchar, 1987), and by the European Space Agency Galileo GNSS constellation with the NeQuick-G model (European, 2016). For these GNSS applications, an accurate description of the plasmaspheric TEC is also required; this is why, many topside ionosphere models include also a plasmasphere extension (Gulyaeva et al., 2002; Stankov et al., 2003; Reinisch et al., 2007; Nava et al., 2008; Prol et al., 2022).

To meet these needs, the International Reference Ionosphere (IRI) community (http://irimodel.org/) is devoting a great deal of effort to improve the modeling of the IRI topside region. IRI is an empirical climatological ionospheric model relying on both ground-based and space-based observations of the ionosphere collected over the last decades on a global basis (Bilitza et al., 2022, and references therein). The IRI project, sponsored by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI), was initiated in 1968. As of April 2014, IRI has been recognized as the official standard for the ionosphere by the International Standardization Organization (ISO) (ISO, 2022). The latest version of IRI, i.e., IRI-2020, includes four options for the modeling of the topside region, which is a testament to the commitment of the IRI community to improve the description of the topside ionosphere. Indeed, among the main additions to the IRI-2020 are the new topside model based on the Bilitza and Xiong (2021) work, and the corresponding plasmaspheric extension based on the topside model merging with empirical plasmasphere models (Gallagher et al., 2000; Ozhogin et al., 2012). This endeavor is motivated by the evidence from different studies (Ezquer et al., 1998; Bilitza and Williamson, 2000; Iwamoto et al., 2002; Trísková et al., 2002; Coísson and Radicella, 2004; Coísson et al., 2006; Bilitza, 2009; Lühr and Xiong, 2010; Klenzing et al., 2011, 2013; Bilitza et al., 2012; Migoya-Orue et al., 2013; Themens et al., 2014; Pignalberi et al., 2016; Themens and Jayachandran, 2016; Themens et al., 2019a, 2019b; Smirnov et al., 2023;
Pezzopane et al., 2023), which pointed out how past IRI topside model options did not adequately capture all plasma variability in the topside.

The motivation of this work is the importance for comparison and validation of the four IRI-2020 topside model options with particular attention to the updates made by the newly introduced topside option by Bilitza and Xiong (2021). Taking advantage of the wealth of in-situ electron density observations collected by several recent LEO satellites in the topside ionosphere, we compared and validated the current four IRI-2020 topside options against in-situ observations taken at different altitudes and covering different local times, seasons, and solar activity levels, on a global scale. Among the available satellite missions, we selected Gravity Recovery and Climate Experiment (GRACE) (Tapley et al., 2004; Xiong et al., 2015), Ionospheric Connection Explorer (ICON) (Heelis et al., 2017; Immel et al., 2018), and Defense Meteorological Satellite Program (DMSP) F15 (Garner et al., 2010), allowing coverage of altitudes between 400 km and 850 km from the ground, for a time window between 1999 and 2022, thus encompassing two solar cycles. Section 2 describes the four IRI-2020 topside options, while Section 3 is devoted to the description of the satellites’ datasets used for the validation along with IRI-2020 runs specification. Section 4 presents the results of the comparison and validation of the four IRI-2020 topside options against satellite observations, by highlighting the spatial, local time, seasonal, and solar activity variations. Section 5 discusses the results and provides some recommendations for future improvements, while Section 6 draws the conclusions along with possible future developments.

## 2. IRI-2020 topside modeling

The latest version of the IRI model is IRI-2020. IRI-2020 includes four options to model the topside ionosphere vertical electron density profile. The mathematical formulation and properties of the four mentioned topside formulations were carefully described by Bilitza et al. (2022); as such, here, only the main information on the models is provided by highlighting the most important differences. IRI-2020 Fortran code is available at the IRI website (http://irimodel.org/).

In IRI, the topside profile is anchored to the F2-layer peak, which is the absolute electron density maximum in the ionosphere. This is characterized by the electron density $NmF2$ at the peak altitude $hmF2$ (orange point in Fig. 1). Starting from the F2-layer peak anchor point, the monotonic decrease in the topside electron density is described by the four topside models (chronologically ordered): IRI-2001, IRI-2001cor, IRI-NeQuick, and IRI-2001cor2. The four models belong to two different families. IRI-2001, IRI-2001cor, and IRI-2001cor2 originated from the Bent et al. (1972) model, with subsequent corrections based on different datasets (Rawer et al., 1978a), while IRI-NeQuick originates from the NeQuick model (Nava

<figure><img src="image_1.png" /><figcaption>Fig. 1. Example of vertical electron density profiles as modeled by the four different topside options of IRI-2020. The black line represents the bottomside region which is common to all the modeled profiles. Topside region profiles are provided as colored curves: grey for IRI-2001, green for IRI-2001cor, red for IRI-2001cor2, and blue for IRI-NeQuick topside option. IRI-2020 was run for the year 2008, day of the year 216, hour UT 05:39:30, latitude 27.53°, longitude -151.86°.</figcaption></figure>

et al., 2008) topside formulation. Therefore, the two topside models’ families have different mathematical formulations and rely on different modeling approaches.

### 2.1. Topside options based on the Bent model

IRI-2001 option is based on the works by (Rawer et al., 1978b; Rawer et al., 1978a) and Rawer (1984) that formulated an analytical description of the Bent et al. (1972) model and included it in earlier IRI versions. Indeed, Bent et al. (1972), taking advantage of topside electron density profiles by Alouette-1 topside sounder satellite, described the topside exponential scale height in three different altitude ranges as a set of graphs. Scale height was described as a function of the F2-layer ordinary critical frequency $foF2$, geomagnetic latitude, and 12-month running mean of monthly $F10.7$ solar radio flux (Tapping, 2013). (Rawer et al., 1978b; Rawer et al., 1978a) and Rawer (1984) applied the Booker function approach (Booker, 1977) to connect analytically and smoothly the scale heights at different altitude ranges. The formulation was later improved by Bilitza (1985). The final result is the IRI-2001 topside model which describes the monotonic decrease of the topside electron density $N_e$, as a function of the height $h$, through an exponential function anchored to the F2-layer peak, with a height-dependent scale height:

$$N_e(h) = NmF2 \cdot \exp[-Y(h)] \quad (1)$$
In Eq. (1), $Y(h)$ was modeled as a function of altitude, geomagnetic latitude, foF2, hmF2, and $F10.7_{365}$, i.e., the 365-day running mean of $F10.7$. For a thorough explanation of the IRI-2001 topside parameters see Bilitza (1990) and Bilitza et al. (2022).

The model was later improved by Bilitza (2004) to fix some discrepancies that, over the years, emerged from the comparison with satellite observations by different authors (Ezquer et al., 1998; Bilitza and Williamson, 2000; Iwamoto et al., 2002; Trísková et al., 2002; Coïsson et al., 2002, 2004). The most critical shortcoming was the overestimation of the electron density at altitudes much higher than the F2-layer peak, particularly for high solar activity level. The correction proposed by Bilitza (2004) resulted in the IRI-2001cor topside model. IRI-2001cor builds on the IRI-2001 formulation (Eq. (1)) by introducing a correction term TCOR in the exponential description:

$$N_e(h) = NmF2 \cdot \exp[-Y(h) + TCOR(h, \text{Modip, LT})] \quad (2)$$

Bilitza (2004) modeled TCOR as a function of $h$, modified dip latitude (Modip, Rawer, 1963), and local time (LT) for the daytime (10–14 LT) and nighttime (22–02 LT) dependence, based on about 120,000 topside profiles from Alouette-1, -2, and ISIS-1, -2 topside sounder satellites. The full description of the TCOR function can be found in Bilitza (2004) and Bilitza et al. (2022). The application of the correction term allowed IRI-2001cor to significantly improve the topside description; in particular, concerning the previously mentioned overestimation at higher altitudes.

Recently, the model was further modified by Bilitza and Xiong (2021) including a solar activity correction term. The need for a solar activity correction arose from several comparison studies which highlighted how, particularly during the 2008 and 2009 very low solar activity level years, IRI significantly overestimated the topside electron density (Lühr and Xiong, 2010; Klenzing et al., 2011, 2013; Bilitza et al., 2012). To overcome this issue, Bilitza and Xiong (2021) introduced the solar activity correction term SCOR to the IRI-2001cor (Eq. (2)) formulation. This is the IRI-2001cor2 topside formulation:

$$N_e(h) = NmF2 \cdot \exp[-Y(h) + TCOR(h, \text{Modip, LT}) + SCOR(PF10.7)] \quad (3)$$

SCOR is a linear function of the PF10.7 solar activity proxy. PF10.7 is the average between the daily F10.7 value and its corresponding 81-day running mean $F10.7_{81}$. Linear coefficients in SCOR describe the altitude, Modip, and LT dependences. These coefficients were obtained by fitting to topside sounder data from Alouette-1, -2, and ISIS-1, -2, and in-situ observations by Challenging Minisatellite Pay-load (CHAMP), GRACE, and Swarm satellites. The full description of the SCOR function can be found in Bilitza and Xiong (2021) and Bilitza et al. (2022). Among the four available options, IRI-2001cor2 is the default in IRI-2020.

IRI topside options based on the Bent model describe the electron density up to 2,000 km. However, as of IRI-

2020 a plasmaspheric extension has been introduced to provide electron density up to GNSS satellites altitude (about 20,000 km). This is based on merging the IRI-2001 family of topside model options with the empirical plasmasphere description provided by either the Gallagher et al. (2000) or the Ozhogin et al. (2012) model through the Booker formalism. Ozhogin et al. (2012) is the recommended default model.

## 2.2. The topside option based on the NeQuick model

IRI-NeQuick topside option was introduced in the IRI-2007 version, and it was the topside default option up to the IRI-2016 version. Unlike IRI-2001 options, IRI-NeQuick is based on the topside formulation of the NeQuick model.

The NeQuick topside model is based on earlier works by Leitinger et al. (2001) and Radicella and Leitinger (2001), which subsequently evolved into the current topside formulation based on a semi-Epstein layer with a variable empirical effective scale height $H$ with altitude (Coïsson et al., 2006, 2009; Nava et al., 2008):

$$N_e(h) = 4NmF2 \frac{\exp\left(\frac{h-hmF2}{H(h)}\right)}{\left[1 + \exp\left(\frac{h-hmF2}{H(h)}\right)\right]^2} \quad (4)$$

with

$$H(h) = H_0 \left[ 1 + \frac{rg(h - hmF2)}{rH_0 + g(h - hmF2)} \right] \quad (5)$$

The topside effective scale height is dependent on three empirical topside parameters: $H_0$, $g$, and $r$ (Nava et al., 2008; Pignalberi et al., 2020b). $H_0$ is the scale height value at the F2-layer peak; $g$ represents the scale height vertical gradient near the F2-layer peak; $r$ is the parameter controlling the $H$ behavior very distant from the F2-layer peak. While $H_0$ modeling is based on F2-layer and bottomside parameters (Nava et al., 2008), $g = 0.125$ and $r = 100$ are kept constant.

Compared to the Bent-based topside options, the NeQuick topside includes a plasmaspheric extension through its $H(h)$ description. Indeed, $H(h)$ was specifically designed to allow for a smooth transition from the linear behavior near the F2-layer peak to the non-linear asymptotic behavior in the overlying plasmasphere through the $r$ parameter. This is because, since the beginning, the NeQuick model was designed for trans-ionospheric applications and TEC calculation up to GNSS satellites heights. Another important difference from the Bent-based options, is the NeQuick scale height connection with the F2-layer bottomside profile through the $H_0$ parameter. Indeed, since $H_0$ depends on the F2-layer bottomside scale height $B_{2\text{bot}}$ (Nava et al., 2008), the topside profile shape is directly linked to the bottomside profile. This is particularly evident at low latitudes where the NeQuick topside mimics the equatorial ionization anomaly double crests latitudinal
behavior also at altitudes much higher than the F2-layer peak (Bilitza, 2009; Pezzopane et al., 2023).

An example of topside profiles modeled by IRI-2020 through the four topside options is provided in Fig. 1, with topside profiles shown with different colors and anchored to the same F2-layer peak point. As clearly shown in Fig. 1, each IRI topside option has a different shape due to different analytical formulations and modeling of the empirical effective scale height embedded in each model.

# 3. Satellite data and IRI-2020 runs

## 3.1. GRACE, ICON, and DMSP F15 satellite data

The GRACE mission (Tapley et al., 2004), jointly implemented by the National Aeronautics and Space Administration (NASA) and Deutsches Zentrum für Luft- und Raumfahrt (DLR) under the NASA Earth System Science Pathfinder Program, comprised two satellites following each other on the same orbital track with a distance of about 200 km. The main scope of the mission was an accurate measure of the Earth's gravity field and its time variability with unprecedented accuracy through a K-Band ranging (KBR) system. The KBR system uses microwaves to accurately measure the distance between the two satellites and the corresponding rate of change. Moreover, the KBR system was set to measure the change of the horizontal TEC between the two satellites, from which it is possible to derive the electron density (Xiong et al., 2010). GRACE satellites were launched on 17 March 2002 into a near-circular polar orbit, with an inclination of 89° and an initial altitude of about 500 km. The GRACE dataset spans about fourteen years from March 2002 to April 2015 (Fig. 2), covering a complete solar cycle from the maximum of the 23rd to the maximum of the 24th solar cycle. During the mission, GRACE altitude decreased from about 500 km at the launch to about 400 km at the end of the mission (Fig. 3a). The GRACE dataset covers all the LTs in

about 161 days (Fig. 3a). The average electron density between the two GRACE satellites was derived by dividing the horizontal TEC by the distance between them considering a bias estimated from CHAMP planar Langmuir probes observations (Xiong et al., 2015). GRACE electron density observations are provided at 15-second time resolution and are publicly available through the Information System and Data Center (ISDC) of GFZ German Research Centre for Geosciences (Xiong et al., 2021).

ICON is a NASA Heliophysics Explorer mission aiming at better characterizing the physical connection between the neutral and ionized atmosphere by quantifying the potential drivers of ionospheric variability originating from the troposphere and stratosphere (Immel et al., 2018). ICON is a single-satellite mission launched on 11 October 2019 into a near-circular orbit with a 27° of inclination, at an initial altitude of around 590 km from the mean sea level, which ended abruptly on 25 November 2022 (Fig. 3b). Among the suite of ICON instruments, our investigation is interested in the ion velocity meter (IVM) which provides in-situ measurements of the ion drift motions, density, temperature, and major ion composition (Heelis et al., 2017). The IVM consists of two planar sensors (A and B), a retarding potential analyzer (RPA) and an ion drift meter (IDM), which allows determining the ions energy and arrival angle, respectively. From RPA measurements, in-situ total ion density is derived at 1 Hz rate (Heelis et al., 2017, 2022; Wu et al., 2023), and assumed to be equal to the electron density (plasma quasi-neutrality assumption). ICON IVM-A data recorded between November 2019 and May 2022 have been used in this paper (Fig. 2). In this time range, the ICON orbit altitude was quite stable in the range 575–605 km and scanned all LTs (Fig. 3b). Unlike the GRACE dataset, the ICON dataset is limited to the equatorial and low latitudes due to the orbital configuration, and the satellite scans several LTs along each orbit. Data collected by ICON are available at https://icon.ssl.berkeley.edu/Data.

<figure><img src="image_2.png" /><figcaption>Fig. 2. Time series of the daily solar activity index F10.7 (blue line), and the corresponding 365-day moving average F10.7<sub>365</sub> (red line). Horizontal colored double arrows mark the GRACE (in green), DMSP F15 (in orange), and ICON (in magenta) datasets time extension.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Fig. 3. Time series of orbit height above Earth's surface and local time at the geographic equator crossing point for GRACE (panel a), ICON (panel b), and DMSP F15 (panel c) satellite datasets. Blue and red points are the heights for ascending and descending orbits, respectively. Green and orange points are the local times for ascending and descending orbits, respectively.</figcaption></figure>

They are also archived at the NASA Space Physics Data Facility (https://spdf.gsfc.nasa.gov) and are freely available through the Coordinated Data Analysis Web (CDAWeb) https://cdaweb.gsfc.nasa.gov/.

DMSP F15 is the 15th satellite of the DMSP program and the first of the block 5D-3 (Garner et al., 2010). DMSP

is a Department of Defense (DoD) program managed by the U.S. Air Force Space and Missile Systems Center (SMC) since 1987. The program designs, builds, launches, and maintains satellites monitoring the meteorological, oceanographic, and solar-terrestrial physics environments. DMSP F15 was launched on 12 December 1999 at an ini-
tial altitude of about 850 km in a quasi-polar Sun-synchronous orbit, with an inclination of 98.9°and ascending and descending nodes at 21:10 LT and 09:10 LT, respectively. DMSP F15 dataset covers more than 21 years, from the launch to August 2021, thus including two solar cycles of observations (Fig. 2). During this long-time period, its orbital plane slightly changed so that ascending and descending nodes varied in the range 15–22 LT and 03–10 LT, respectively, while the orbit altitude was quite stable in the range 830–855 km (Fig. 3c). DMSP satellites carry the Special Sensors-Ions, Electrons, and Scintillation (SSIES) thermal plasma analysis package, which is a suite of instruments built by the Center for Space Sciences at the University of Texas at Dallas. SSIES includes a RPA, an IDM, a scintillation meter, and a Langmuir probe (Rich, 1994). In this study, we used in-situ electron density observations collected by DMSP F15 Langmuir probe at 1 Hz rate. Data was gathered from the CEDAR Madrigal database at http://cedar.openmadrigal.org/.

## 3.2. IRI-2020 runs

IRI-2020 was run along the GRACE, ICON, and DMSP F15 satellite orbits with the same time and spatial resolution of satellites' observations. In this way, a one-to-one comparison between measured and modeled values is guaranteed. Specifically, for each satellite observation, the F2-layer anchor point was modeled through the IRI-2020 default options, i.e., through the use of URSI coefficients (Rush et al., 1989) in the IRI spherical harmonics description of NmF2 (Jones and Gallet, 1962, 1965; Jones et al., 1969), and the Shubin (2015) option for hmF2, with solar and geomagnetic indices provided by E-CHAIM website (https://chain-new.net/). The F2-layer storm model (Fuller-Rowell et al., 2000; Araujo-Pradere et al., 2002) was activated. Thereafter, the topside profile was modeled through the four topside options (see Section 2) anchored to the same F2-layer peak anchor point, and the N_c value at the satellite altitude was considered for comparison.

Since topside N_c values modeled by IRI need the specification of the F2-layer peak anchor point, which is provided by IRI itself, this introduces an uncertainty in the validation process against satellite-measured N_c values. Indeed, errors in the F2-layer peak, both in NmF2 and hmF2, propagate to the N_c values modeled at the satellite altitude. This source of uncertainty cannot be mitigated with the available in-situ observations collected by satellites. However, over the years, IRI model performance was assessed in many studies performed by different groups, which highlighted a satisfactory IRI performance in predicting the F2-layer peak characteristics. For a detailed validation of IRI F2-layer peak characteristics against ionosondes and Constellation Observing System for Meteorology, Ionosphere and Climate/Formosa Satellite 3 (COSMIC/FORMOSAT-3) radio occultation observations, refer to Pignalberi et al. (2021). Regarding the

Shubin (2015) option for hmF2, its performances when compared to other hmF2 modeling options have been assessed by several studies and presented satisfactory results (Mengist et al., 2020; Huang et al., 2021; Moses et al., 2021; Scotto et al., 2023). Moreover, the IRI was compared with other empirical and physics-based models, achieving in most of the cases the best, or at least on par with the best theoretical and assimilative models, predictions of NmF2 and hmF2 (Shim et al., 2011,2012, 2017,2018).

# 4. Validation of the IRI-2020 topside ionosphere options

## 4.1. Overall perspective

To provide an overall perspective on the performance of the four different IRI-2020 topside options, several statistical metrics have been calculated based on the entire LEO satellites' datasets, irrespective of location, LT, season, and solar activity level. In particular, we rely on the ratios between IRI-modeled and satellite-measured in-situ N_c values:

$$ \text{Ratio}_{i,j} = \frac{\text{Modeled } N_{c,i}}{\text{Measured } N_{c,j}} \qquad (6) $$

with i = (IRI-2001, IRI-2001cor, IRI-2001cor2, IRI-NeQuick) and j = (GRACE, ICON, DMSP F15).

Ratios enable a comparison of N_c values collected under different geophysical conditions, i.e., location, LT, season, and solar activity level. Furthermore, ratios facilitate comparison of values obtained at different altitudes, i.e., for different LEO satellites. A perfect model should provide ratios equal to unity, irrespective of different geophysical conditions. If so, the model would be able to properly describe all the variations embedded in the measurements. Ratios in excess of unity indicate an overestimation by the model, contrary to ratio values below unity indicating an underestimation by the model. Furthermore, any trends in ratios, as a function of a specific parameter, testifies a weakness of the model in correctly describing the variation associated to that parameter.

Statistics on ratios are provided in Table 1, with corresponding probability density functions (PDFs) and joint probability distributions (JPDs) in Fig. 4, for all the i and j combinations. From Table 1 and Fig. 4, it is evident how the performance of IRI-2020 topside options is sensitively dependent on the altitude above the F2-layer peak. Specifically, as we ascend higher from the F2-layer peak altitude and dive into the topside ionosphere, the performance of IRI-2020 topside options generally degrades. The best agreement with observations is evident at GRACE altitudes (400–520 km) which is the nearest to the F2-layer peak. Moreover, at GRACE altitudes, the performance of the four topside options is quite similar. This is due to the fact that, by design, the topside profile is anchored to the F2-layer peak, which is the same for all the topside options, and GRACE is not so far from it.
<table><caption>Table 1
Ratio statistics between IRI-modeled and satellite-measured electron density values for GRACE, ICON, and DMSP F15 datasets.</caption><thead><tr><th></th><th>IRI-2001</th><th>IRI-2001cor</th><th>IRI-2001cor2</th><th>IRI-NeQuick</th></tr></thead><tbody><tr><td colspan="5"><strong>GRACE (400–520 km)</strong></td></tr><tr><td>Median</td><td>1.191</td><td>1.178</td><td>1.034</td><td>1.041</td></tr><tr><td>Inter-quartile range</td><td>0.905</td><td>0.885</td><td>0.706</td><td>0.753</td></tr><tr><td>Percentile 5th</td><td>0.544</td><td>0.537</td><td>0.477</td><td>0.448</td></tr><tr><td>Percentile 25th</td><td>0.858</td><td>0.850</td><td>0.759</td><td>0.748</td></tr><tr><td>Percentile 75th</td><td>1.763</td><td>1.736</td><td>1.465</td><td>1.501</td></tr><tr><td>Percentile 95th</td><td>3.500</td><td>3.367</td><td>2.793</td><td>2.766</td></tr><tr><td>Total counts</td><td>75,223,896</td><td>75,223,896</td><td>75,223,896</td><td>75,223,896</td></tr><tr><td colspan="5"><strong>ICON (575–605 km)</strong></td></tr><tr><td>Median</td><td>1.522</td><td>1.314</td><td>0.799</td><td>1.063</td></tr><tr><td>Inter-quartile range</td><td>1.235</td><td>1.015</td><td>0.523</td><td>0.859</td></tr><tr><td>Percentile 5th</td><td>0.576</td><td>0.496</td><td>0.357</td><td>0.337</td></tr><tr><td>Percentile 25th</td><td>1.022</td><td>0.890</td><td>0.581</td><td>0.695</td></tr><tr><td>Percentile 75th</td><td>2.258</td><td>1.905</td><td>1.104</td><td>1.553</td></tr><tr><td>Percentile 95th</td><td>3.887</td><td>3.078</td><td>1.899</td><td>2.446</td></tr><tr><td>Total counts</td><td>76,998,272</td><td>76,998,272</td><td>76,998,272</td><td>76,998,272</td></tr><tr><td colspan="5"><strong>DMSP F15 (830–855 km)</strong></td></tr><tr><td>Median</td><td>1.675</td><td>1.145</td><td>0.896</td><td>0.879</td></tr><tr><td>Inter-quartile range</td><td>2.069</td><td>1.201</td><td>0.851</td><td>0.772</td></tr><tr><td>Percentile 5th</td><td>0.604</td><td>0.428</td><td>0.340</td><td>0.277</td></tr><tr><td>Percentile 25th</td><td>1.032</td><td>0.745</td><td>0.614</td><td>0.581</td></tr><tr><td>Percentile 75th</td><td>3.101</td><td>1.946</td><td>1.465</td><td>1.353</td></tr><tr><td>Percentile 95th</td><td>7.910</td><td>4.789</td><td>4.138</td><td>2.875</td></tr><tr><td>Total counts</td><td>621,493,692</td><td>621,493,692</td><td>621,493,692</td><td>621,493,692</td></tr></tbody></table>

Consequently, at these altitudes the F2-layer peak anchor point modeling has a more relevant role than the modeling of the topside shape function, which instead becomes more and more important at increasing altitudes. On the other hand, the high accuracy of topside options at GRACE altitudes is also an indirect confirmation that IRI NmF2 and hmF2 modeling is robust. About the dispersion of modeled data, percentiles and inter-quartile range (IQR) values show as the most recent topside options, i.e., IRI-NeQuick and IRI-2001cor2, reduce the dispersion of data at GRACE altitudes. This feature is shared among the three satellites' datasets at different altitudes, and signifies the improvement brought by the IRI-NeQuick and IRI-2001cor2 options on the description of the plasma variations under different geophysical conditions. In this respect, the largest improvement is visible at ICON altitudes where the IRI-2001cor2 option diminishes the dispersion providing a narrower distribution. However, for the same conditions, IRI-2001cor2 shows a noticeable underestimation compared to other options and to IRI-NeQuick in particular, which instead shows a good accuracy but lower precision. At the highest altitudes analyzed in this study, i.e., those of DMSP F15, IRI topside options exhibit the largest discrepancies from observations in both accuracy and dispersion, with IRI-NeQuick and IRI-2001cor2 providing the best performance. By comparing the Bent-based topside options, we can see how any subsequent correction brought to the IRI-2001 model was in the direction of lowering $N_e$

values. Although this is justified by IRI-2001 and IRI-2001cor median overestimation at any altitude, the latest correction, IRI-2001cor2, seems to excessively reduce $N_e$ values at higher altitudes, particularly in the ICON's altitude range (at around 600 km). It is worth remarking that differences in the IRI options performance against different satellites, as highlighted by the overall statistics shown in Table 1, are not only due to the different altitude sensed by GRACE, ICON, and DMSP F15. Indeed, ICON dataset covers only the equatorial and low latitudes, while GRACE and DMSP F15 cover also mid and high latitudes. DMSP F15 collected data in the range 03–10 LT and 15–22 LT, while GRACE and ICON sampled all LTs. In addition, the three datasets covered different solar activity levels. Therefore, the overall statistics here reported have to be properly complemented with analyses highlighting also the performance variation with solar activity, LT, latitude, and season. This is the subject of the following subsections.

Unlike PDFs, JPDs give information about the agreement between models and observations at different ranges of $N_e$ values. In the right panels of Fig. 4, IRI-modeled median values for a selected satellite-measured $N_e$ range are plotted versus the satellite $N_e$ observations and represented as colored points, with corresponding interquartile ranges as error bars. All options are included in each plot to be able to compare different IRI-2020 topside options. It is worth noting that most of the $N_e$ values lie in
<figure><img src="image_4.png" /><figcaption>Fig. 4. Left panels: probability density functions of ratios between IRI-modeled and satellite-measured electron density values. Panel a) for the GRACE dataset, panel c) for the ICON dataset, and panel e) for the DMSP F15 dataset. Vertical dashed lines represent the ratio equal to unity. Right panels: joint probability distributions between IRI-modeled (y-axis) and satellite-measured (x-axis) electron density values. Panel b) for the GRACE dataset, panel d) for the ICON dataset, and panel f) for the DMSP F15 dataset. Colored points represent the IRI-modeled conditioned median values for a selected satellite-measured electron density range, with corresponding inter-quartile ranges as error bars. Slant dashed lines represent the locus of points for which the ratio is equal to unity. In each panel, grey values are associated with IRI-2001, green with IRI-2001cor, red with IRI-2001cor2, and blue with IRI-NeQuick.</figcaption></figure>

the range $10^4–10^6 \text{ cm}^{-3}$ for GRACE and ICON datasets, and in the range $10^{3.5}–10^5 \text{ cm}^{-3}$ for the DMSP F15 dataset (corresponding counts are not shown in the plots). In the

JPDs, we identify different behavior as a function of $N_e$. In the range where most of the observations lie, IRI-modeled and satellite-measured $N_e$ values are mostly lin-
early related. On the other hand, at the lower values edge of the distributions IRI persistently overestimates measurements, while at the higher values edge IRI underestimates them, irrespective of the topside option used. Since this behavior is independent of the topside model option, it could be associated to a mismodeling by IRI (but not related to the topside formulation used) or, alternatively, to satellite instrumental issues. From the modeling side, the overestimation at low densities could be ascribed to a mismodeling of the F2-layer peak anchor point by IRI, or to phenomena not encapsulated by the climatological description provided by IRI. From the observations side, it is worth pointing out that satellite $N_e$ observations below about $10^3 \text{ cm}^{-3}$ are at the lower edge of instruments range of measurement. Consequently, for such low $N_e$ values a contamination of unreliable observations by satellite instrumentation limitations cannot be excluded. A clue about the issue is provided by the similarity of the ICON and DMSP F15 plots (Fig. 4d and 4f) and significant difference to the GRACE plots (Fig. 4b), especially at low densities where both techniques reach limitations. Such differences are probably due to the different way GRACE derive $N_e$, based on KBR measurements, compared to in-situ probing by RPA and LP on-board ICON and DMSP F15, respectively. The largest uncertainty in satellite observations introduced at very low densities would largely explain the high deviations between model and observations at low densities which, however, have a negligible impact on the overall performance because they affect a very small number of cases. At GRACE altitudes, the linear dependence among IRI topside options and observations is quite remarkable and is supported by the results of the corresponding PDFs. It is worth noting how the IRI-2001cor2 option shows a much consistent linear relation with observations at ICON altitudes, albeit with the already mentioned general underestimation.

## 4.2. Dependence on solar activity

The time extent of the GRACE and DMSP F15 datasets allows to investigate to what extent the IRI topside options capture the solar activity cycle variation observed by the satellites. Fig. 5 shows a time series of median ratios between IRI-modeled and DMSP F15-measured electron density values, which are overplotted on two-dimensionally binned ratio counts, with IQR values as error bars. To further investigate variations with solar activity, Fig. 6 shows how the ratio values behave as a function of the F10.7 solar activity proxy. Fig. 7 shows the same analysis shown in Fig. 5 but for the GRACE dataset.

At DMSP F15 altitudes (Fig. 5), the IRI-2020 topside options show different deviation trends as a function of time, i.e., solar activity. By looking at median values (black points) and at the envelopes of the bins with more counts (red and orange bins), it appears that all four options still exhibit deviations from the DMSP F15 observations, with

the IRI-2001 option showing the largest deviations and the IRI-NeQuick option showing the smallest deviations. IRI-2001 overestimates the observations over the whole time span. IRI-2001cor and then IRI-2001cor2 bring the deviations closer to unity and thus successively improve the solar cycle representation of the IRI topside. For all four options, the deviations still exhibit variations with the solar cycle, most markedly seen in the envelope around the upper and lower boundaries of the data scatter. The median of the ratios maximizes for high solar activity years (2000–2002 and 2013–2015) and minimizes for low solar activity years (2007–2009 and 2019–2021). This correlation with the solar activity persists for all three IRI-2001 options and in fact is slightly more pronounced in IRI-2001cor2. The IRI-NeQuick option shows a different behavior with median values around the ratio equal to unity but showing variations which do not seem associated with the solar activity cycle variation or, at least, they are not in phase with the solar activity. When plotting ratios against F10.7 (Fig. 6) it becomes clear that IRI-2001cor2 shows a definite trend with solar activity. Specifically, ratios between IRI-2001cor2 and DMSP F15 show a quasi-linear increase with solar activity (Fig. 6c). IRI-2001cor2 median values are in the range 0.7–0.8 for low solar activity (F10.7 below 85 sfu), around the unity for mid solar activity (F10.7 between about 90 and 120 sfu), and increasingly over the unity at higher solar activity level. At GRACE altitudes (Fig. 7), the variation with solar activity is well described by all the IRI-2020 topside options with median values mostly around unity and with a dispersion lower than at DMSP F15 altitudes. These results agree with those shown in Section 4.1 and indicate that the solar activity variation of the F2 peak values is well represented in IRI using the URSI model option. For all modeled values, the last years of the GRACE mission (2012–2015) show the largest dispersion. These are the years when GRACE altitude decreased to about 400 km (see Fig. 3a). The largest dispersion for years 2012–2015 is probably due to the large GRACE altitude variation for that period.

## 4.3. Dependence on latitude, local time, and season

An approach similar to that adopted to obtain Figs. 5 to 7 has been applied to study the ratio variations with latitude, local time, and season. Since data used in this study concern the topside ionosphere, we use geomagnetic coordinates; specifically, Quasi-Dipole (QD) geomagnetic latitude and Magnetic Local Time (MLT) (Laundal and Richmond, 2017). Indeed, plasma dynamics in the topside ionosphere is mainly driven by the plasma ambipolar diffusion along geomagnetic field lines (Bauer, 1969; Pignalberi et al., 2020a), which makes the use of geomagnetic coordinates the natural basis to represent plasma variations at these altitudes.

Figs. 8 to 10 show ratios as a function of the QD latitude for GRACE, ICON, and DMSP F15 datasets, respectively.
<figure><img src="image_5.png" /><figcaption>Fig. 5. Time series of ratios between IRI-modeled and DMSP F15-measured electron density values as a function of time. The color represents the counts inside each bin in logarithmic scale. Black points and error bars represent the median and inter-quartile range values for specific periods. Horizontal black dashed line represents the value of the ratio equal to unity. Panel a) for IRI-2001, panel b) for IRI-2001cor, panel c) for IRI-2001cor2, and panel d) for IRI-NeQuick.</figcaption></figure>

While GRACE and DMSP F15 datasets cover the entire spectrum of QD latitude range, ICON is restricted to the range ± 40° by orbital configuration. Fig. 8 shows how the IRI-2001cor2 model provides a very accurate description of the latitudinal variation at GRACE altitudes, with median values very close to unity at all latitudes. In the same conditions, the other topside options also show a reasonable agreement with GRACE observations, but all of them show an evident overestimation at low latitudes. Specifically, this overestimation has a double-hump structure with maxima located at QD latitudes corresponding to the equatorial ionization anomaly (EIA) crests, i.e., at around ± 15° QD latitude. The latest correction brought to IRI-2001, e.g., IRI-2001cor2, has been particularly effective in correcting this issue. The same phenomenology is visible also at higher altitudes, for ICON in Fig. 9 and for DMSP F15 in Fig. 10, with IRI-2001cor2 improving the low latitudes description at different altitude ranges. At DMSP F15 altitudes, variations with latitudes are more marked with topside options showing the best agreement at mid latitudes. This is due not only to an easier predictability of ionosphere plasma conditions at mid latitudes compared to low and high latitudes (Zolesi and Cander, 2014), but also to the abundance of mid-latitude observa-

tions used to develop the IRI topside models (Bilitza et al., 2022). At higher altitudes, IRI-NeQuick shows the best agreement with observations at different QD latitudes, with the lowest dispersion. IRI-2001cor2 remarkably improves the description by IRI-2001-based options at low latitudes, while the same cannot be said for high latitudes.

To characterize the local time variation, we explicitly sorted ratios as a function of both QD latitude and MLT, and calculated median ratio values for all possible QD latitude and MLT combinations. Figs. 11 and 12 show these median values as a function of the QD latitude (on y-axis) and MLT (on x-axis), for the GRACE and ICON datasets, respectively. This analysis was not performed on the DMSP F15 dataset because, due to the satellite orbital configuration, it covers only very few MLTs.

Focusing on low latitudes, the comparison with GRACE and ICON datasets shows consistent results at different altitudes, i.e., both the latitudinal and diurnal patterns are similar albeit with possibly different values. Each IRI topside option shows a remarkable overestimation around sunrise at low latitudes. This is probably associated to the phenomenology related to the equatorial morning overshoot which gives rise to very high electron tempera-
<figure><img src="image_6.png" /><figcaption>Fig. 6. Ratios between IRI-modeled and DMSP F15-measured electron density values as a function of the F10.7 solar activity proxy. The color represents the counts inside each bin in logarithmic scale. Black points and error bars represent the median and inter-quartile range values for specific F10.7 values. Horizontal black dashed line represents the value of the ratio equal to unity. Panel a) for IRI-2001, panel b) for IRI-2001cor, panel c) for IRI-2001cor2, and panel d) for IRI-NeQuick.</figcaption></figure>

tures associated to low electron densities (Stolle et al., 2011), and a decrease of *lmF2* caused by the combined action of downward plasma vertical **E** × **B** drift and neutral winds (Oyama et al., 1996). The IRI model fails in properly describing these complex ionospheric dynamics and their effect on F2-layer peak characteristics at low latitudes (Pignalberi et al., 2021). The fact that the overestimation feature is common to each topside option underlines that this aspect can be attributed to the modeling of the F2-layer peak characteristics rather than to the topside profile shape formulation. The QD lat. vs. MLT plot clearly highlights how the modeling of the EIA in the topside is a complex task. Indeed, IRI-2001, IRI-2001cor, and IRI-NeQuick options show a clear signature connected to the EIA phenomenon, i.e., a general overestimation at QD latitudes associated to the EIA crests (mostly between 10° and 20° QD latitude in both hemispheres), and an underestimation at the trough over the geomagnetic equator, according to the MLT variation usually characterizing the EIA development (Balan et al., 2018). IRI-2001cor2 is in the best agreement to the data in describing the topside ionospheric variation associated with the EIA, both in QD latitude and MLT, with ratio median values

mostly around unity or slightly underestimated. Fig. 11 shows that the mid latitudes are well described by the topside models, with slight diurnal variations. At high latitudes the diurnal variation is well captured by all models but with a persistent slight underestimation.

To characterize possible seasonal variations not described by IRI topside models, ratio values were studied also as a function of the day of the year (DOY). Figs. 13 and 14 show corresponding medians as a function of the QD latitude (on y-axis) and DOY (on x-axis), for the GRACE and DMSP F15 datasets, respectively. This analysis was not performed on ICON dataset due to the limited timespan of the dataset extension which did not allow homogeneous sampling of different seasons.

At GRACE altitudes (Fig. 13), as previously highlighted, differences among topside options are slight and they exhibit similar seasonal patterns. In particular, we can identify different seasonal patterns for low latitudes compared to mid and high latitudes. Mid and high latitudes are generally characterized by an underestimation pattern in the summer hemisphere and an overestimation pattern in the winter hemisphere. Instead, low latitudes show a general underestimation irrespective of season, with
<figure><img src="image_7.png" /><figcaption>Fig. 7. Same as Fig. 5 but for the GRACE dataset.</figcaption></figure>

a superposed latitudinal modulation. When considering DMSP F15 altitudes (Fig. 14), the differences between models and observations sensibly increase. However, besides the ratio magnitude, seasonal patterns at DMSP F15 altitudes are similar to those at GRACE altitudes. The seasonal variation showing an underestimation in the summer hemisphere and an overestimation in the winter hemisphere, at mid and high latitudes, is well defined for IRI-2001 and IRI-2001cor, while it is strongly reduced by IRI-2001cor2 and IRI-NeQuick. IRI-2001cor2 still shows a seasonal variation but confined to auroral latitudes, as well as IRI-NeQuick does but to a minor extent. At low latitudes the seasonal variation is less marked, with a general overestimation by IRI-2001 and IRI-2001cor, and a better agreement by IRI-2001cor2 and IRI-NeQuick.

## 5. Discussion

This extensive study with a large volume of in-situ satellite observations was undertaken with the goal to contribute to future improvements of the IRI topside formalism. To this end, we have studied the variations of the model-observations ratio versus solar activity, latitude, local time, and season. Results of the validation against GRACE, ICON, and DMSP F15 satellites demonstrated that the two most recent IRI topside options, i.e., IRI-

NeQuick and IRI-2001cor2, show the highest performance in the modeling of the electron density variations in the topside ionosphere. At the same time, the comparison highlighted that none of them can properly predict the entire range of variations exhibited by LEO satellite observations for different latitude, local time, altitude, season, and solar activity. This testifies that the empirical modeling of the topside ionosphere has room for improvement based on new datasets and/or different modeling techniques and parameterizations.

IRI-2020 introduced the IRI-2001cor2 model as the default and recommended topside option (Bilitza et al., 2022). This option introduced a solar activity correction term in the IRI-2001 topside formulation based on topside sounder data from Alouette-1, -2, and ISIS-1, -2, and in-situ observations by CHAMP, GRACE, and Swarm LEO satellites (Bilitza and Xiong, 2021). Moreover, IRI-2001cor2 took advantage from the inclusion of LEO satellites in-situ observations in its underlying dataset to improve the representation of both the latitudinal and local time variation of topside electron density, particularly at low latitudes. Our results confirm that IRI-2001cor2 mostly succeeded in this. Indeed, previous topside options, including IRI-NeQuick, have difficulty in properly representing the latitudinal variation of topside electron density at low latitudes and at the LTs of the EIA, as previously
<figure><img src="image_8.png" /><figcaption>Fig. 8. Ratios between IRI-modeled and GRACE-measured electron density values as a function of Quasi-Dipole magnetic latitude. The color represents the counts inside each bin in logarithmic scale. Black points and error bars represent the median and inter-quartile range values for specific latitudes. Horizontal black dashed line represents the value of the ratio equal to unity. Panel a) for IRI-2001, panel b) for IRI-2001cor, panel c) for IRI-2001cor2, and panel d) for IRI-NeQuick.</figcaption></figure>

demonstrated by Bilitza (2009) and Pezzopane et al. (2023). Instead, IRI-2001cor2 better describes both the latitudinal and LT variations at low latitudes. Our study highlights the steady improvement achieved for the IRI topside electron density through progression from IRI-2001 to IRI-2001cor to IRI-2001cor2. Unlike other options, which exhibit highest overestimations near the EIA peaks, the IRI-2001cor2 reaches its highest overestimation values at the geomagnetic equator. This indicates that the newest IRI topside option did account well for the electron density variation near the EIA crests and their shift towards the geomagnetic equator with increasing altitude, but it did somewhat overestimate the density near the geomagnetic equator. The geomagnetic equator is an anchor point in the description of the latitudinal dependence of the parameters used by Bilitza and Xiong (2021) in the IRI-2001cor2 model. Specifically, they described the latitudinal variation of the correction factor in Eq. (3) through Modip coordinates with anchor points at 0°, ±25°, ±60°, and ±90°. Modip and QD latitude converge at the geomagnetic equator, while 25° in Modip coordinate is around 15° in QD latitude. The effect of the low-latitude anchor points is visible in Fig. 8–10 where IRI-2001cor2 ratio median values (panels c) show a relative maximum at the geomagnetic equator

and relative minima at around ± 15° QD latitude, with too sharp transitions between them, all features that are not present in previous IRI-2001 formulations. The latitudinal dependence of the parameters included in the IRI-2001cor2, albeit remarkably mitigating the previous issues connected to the EIA representation, would benefit from further improvements to smooth out these anomalous latitudinal transitions.

Our results evidenced that the improvement by IRI-2001cor2 is altitude dependent. Specifically, the improvement is particularly evident at GRACE and ICON altitudes (in the range 400–600 km), while at DMSP F15 altitude (in the range 830–850 km) it is marginal compared to IRI-NeQuick. Indeed, at DMSP F15 altitude IRI-2001cor2 shows deviations from observations that are in phase with the solar cycle, slightly underestimating and overestimating measurements respectively at low and high solar activity. This feature is mostly to be ascribed to the dataset used by Bilitza and Xiong (2021) for the introduction of the solar activity term in Eq. (3), which is biased towards the altitudes covered by CHAMP, GRACE, and Swarm satellites, i.e., in the range 330–520 km. In IRI-2001cor2, the DMSP F15 altitude range is exclusively based on the Alouette and ISIS topside sounder data and
<figure><img src="image_9.png" /><figcaption>Fig. 9. Same as Fig. 8 but for the ICON dataset.</figcaption></figure>

somewhat limited by the spatial and temporal extent of the data established by analyzing the topside sounder ionograms (Bilitza et al., 2004). Including data from the DMSP series of satellites may help to establish a new set of model coefficients, which would significantly improve the model in the upper topside and facilitate the connection to the new plasmaspheric extension of the IRI model (Bilitza et al., 2022).

The solar activity dependence shown by the IRI-2001cor2 option when compared to DMSP F15 is somewhat unexpected because the latest correction of the IRI-2001 model was introduced with the main goal of improving the solar activity description of the model, particularly under low solar activity levels. Bilitza and Xiong (2021) performed a self-validation of the IRI-2001cor2 model against the topside sounders and LEO satellites observations used to develop the solar activity correction term itself. This validation demonstrated the significant improvement of IRI-2001cor2 over IRI-2001cor, highlighted by Fig. 8–12 in Bilitza and Xiong (2021). However, the validation performed by Bilitza and Xiong (2021) is limited to the LTs 10–14 and Modip within ± 30°. The LT variation in the SCOR term in Eq. (3) was estimated through observations in a daytime range (10–14 LT) and nighttime range (22–02 LT), and it was assumed a constant behavior of LT coefficients for the daytime and nighttime

sectors with continuous transitions at sunrise and sunset through Epstein functions of zero order (for details see Appendix A in Bilitza et al., 2022). Since DMSP F15 dataset mostly concerns observations taken around the solar terminator hours (see Fig. 3c), the solar activity dependence of IRI-2001cor2 ratios (Fig. 6c) could be a side-effect of an underrepresented LT variation of the solar activity correction term in Eq. (3). On the contrary, the comparison with GRACE observations at a lower altitude and covering all LTs, showed a much better agreement and no solar activity trends in the comparison. To get a clearer and definitive view of the solar activity variations in the upper topside region, the comparison with satellite observations recorded at different LTs and altitudes, and covering different solar cycles, is required in the future studies.

The present study has shown that the IRI-NeQuick topside option is a reliable model irrespective of altitude. Currently, the NeQuick topside model is entirely specified as a function of solar activity and F2-layer peak parameters (Nava et al., 2008). This limits the range of $H_0$ values that could be represented, particularly given that the topside thickness tends to have maxima in the morning and evening, which is largely orthogonal to the variability in *hmF2* and *foF2*. As shown in Pignalberi et al. (2018) and Pezzopane and Pignalberi (2019), the relationship between $H_0$ and peak parameters, *hmF2* and *NmF2*, is not particu-
<figure><img src="image_10.png" /><figcaption>Fig. 10. Same as Fig. 8 but for the DMSP F15 dataset.</figcaption></figure>

larly linear. Accounting for some of these limitations in the current formulation would likely result in an improvement. Further improvement could be achieved by including models of the NeQuick *r* and *g* parameters, which themselves vary in both time and space (Pignalberi et al., 2022a). Themens et al. (2018) demonstrated that other values of *r* and *g* are more optimal at high latitudes, while Prol et al. (2022) and Pignalberi et al. (2023) have shown that the slope of the scale thickness near the F2 peak (effectively *g*) varies strongly. Both these modifications to the model formalism would likely improve performance and allow the model to correctly transition the equatorial anomaly crests into a single peak with increasing altitude, therefore leading to a more realistic, even though still simplified, geometric field-aligned formulation of the plasmasphere electron density above about 2,000 km. In this framework, Pezzopane et al. (2023), based on the findings by Pignalberi et al., (2022a), have recently shown that there exist suitable combinations of the three NeQuick topside parameters (*H*₀, *g*, and *r*) that properly face this low-latitude NeQuick mismodeling. Further evidence about future improvements to the NeQuick topside formulation have been also provided by Pignalberi et al. (2024) by assimilating measured ionospheric equivalent slab thickness (Pignalberi et al., 2022b) values into NeQuick to constrain the *B*₂bot thickness parameter (on which *H*₀ depends). This study evidenced

that, limited to the mid latitudes investigated by the study, NeQuick mostly underestimates *B*₂bot and, consequently, also the topside scale height (Eq. (5)) is underestimated. The underestimation affects mainly the nightside sector and increases as the solar activity decreases, which largely agrees with our results and with Kashcheyev and Nava (2019). Most of the NeQuick issues evidenced by our validation and by previous studies can be mitigated, if not solved, by a more refined specification of the NeQuick topside parameters from which the effective topside scale height (Eq. (5)) depends, and by relaxing the current link between the bottomside and topside thickness parameters.

Our investigation mostly focused on low and mid latitudes. However, GRACE and DMSP F15 datasets also facilitated insights on the models' performance at high latitudes. It is well-established that the IRI model is mostly based on data collected mainly at mid and low latitudes (Bilitza et al., 2022), while some particular high-latitude ionospheric features are underrepresented in the model. To alleviate some of the IRI topside issues highlighted by Themens et al. (2014), the *Empirical Canadian High Arctic Ionospheric Model* (E-CHAIM) was developed as a high-latitude alternative (Themens et al., 2017, 2018, 2019a). Comparisons between E-CHAIM and the IRI-NeQuick with topside in-situ measurements from DMSPs and CHAMP (Themens et al., 2019a, Themens et al., 2019b)
<figure><img src="image_11.png" /><figcaption>Fig. 11. Ratios between IRI-modeled and GRACE-measured electron density values as a function of the Quasi-Dipole magnetic latitude (y-axis) and the magnetic local time (x-axis). The color represents the median value (in logarithmic scale) of the ratios inside each bin. Panel a) for IRI-2001, panel b) for IRI-2001cor, panel c) for IRI-2001cor2, and panel d) for IRI-NeQuick.</figcaption></figure>

and Swarm (Themens et al., 2021) satellites have been con-
ducted in the past, demonstrating generally large electron
density errors by the IRI-NeQuick in the upper topside
during summer and high solar activity conditions, where
electron density is strongly underestimated and E-
CHAIM demonstrated considerable improvement. Densi-
ties from both models, however, converged during the win-
ter, with an overestimation of the electron density at
DMSPs altitude. The overall improvement made by E-
CHAIM at DMSPs altitude is in contrast to results much
closer to the F2 peak in comparisons to CHAMP and
Swarm, where E-CHAIM only provided a slight improve-
ment over the IRI-NeQuick. More modest errors in the
near-peak topside were attributed to an overall underesti-
mation of NmF2 by the IRI in those regions counteracting
an overestimation of the near-peak topside shape within
the IRI-NeQuick, whereby the shape of the topside would
then underestimate electron density at altitudes more
than ~ 200 km above the F2 peak. The results here pre-
sented are very consistent with these previous high-
latitude studies and suggest the IRI-2001cor2 option likely
performs more comparably to E-CHAIM during summer
conditions at DMSPs altitudes, but likely now performs
worse than E-CHAIM during winter conditions. An inde-

pendent assessment would, however, be necessary to deter-
mine this conclusively. In E-CHAIM, the topside model
includes geomagnetic forcing in the characterization of
the topside thickness and the peak density. This is particu-
larly critical at high latitudes, as auroral heating can cause
substantial expansion of the topside ionosphere, whereby
the thickness can increase by a factor of two or more
(Themens et al., 2018). This increase in thickness is, how-
ever, often also accompanied by an overall decrease in peak
electron density and an increase in peak altitude, which
would suggest that any effort to include geomagnetic forc-
ing in the IRI topside thickness should be accompanied by
self-consistent driving of the peak density and height. In
the absence of geomagnetic forcing models for all three ele-
ments of the profile, the inclusion of a geomagnetic forcing
in any individual element may result in an overall worse
representation of electron density, even if the layer shapes
are better represented.

As mentioned in Section 3.2, for each satellite observa-
tion, the F2-layer anchor point was modeled through the
IRI-2020 default options. Therefore, the uncertainty in
the F2-layer peak values (for both NmF2 and hmF2) was
subsequently reflected as an uncertainty on the Ne value
modeled at the satellite altitude during the validation pro-
<figure><img src="image_12.png" /><figcaption>Fig. 12. Same as Fig. 11 but for the ICON dataset.</figcaption></figure>

To overcome this uncertainty and perform a more accurate topside validation study, in the near future we intend to exploit COSMIC-1 and COSMIC-2 electron density profiles which are validated against a global ionosonde electron density profile dataset. Since the inversion error is systematically accumulated from the top to the bottom of the radio occultation profile, when F2-layer peak parameters match those measured by a co-located ionosonde, it is expected that the full topside segment of the radio occultation profile is correctly estimated (Haralambous and Oikonomou, 2013). This hypothesis was verified using incoherent scatter radar measurements and corresponding co-located radio occultation profiles with matched peak parameter values in a study by Shaikh et al. (2018). It is also worth noting that, in any anchor-based formalism, errors in peak parameters and layer thicknesses can interact in both constructive and destructive manners. In Themens et al. (2021), E-CHAIM, which uses a slightly modified version of the NeQuick topside formalism, was shown to produce moderate errors in the topside, while only having relatively small errors in *hmF2* and *NmF2*. It was shown that despite the *hmF2* and *NmF2* error being small, the error in these parameters were of the same sign when considering their contribution to topside electron density, ultimately resulting in larger overall errors in the

near-peak topside. Further work leveraging full electron density profiles is thereby ultimately necessary in order to properly understand and correct the errors in the IRI.

Although the topside ionosphere region is essential to provide accurate TEC values, the achievement of accurate TEC estimations also demands advancements in describing the electron content of the plasmasphere. This would increase the overall applicability of the IRI model to satellite-based navigation systems. Presently, this challenge persists as existing ionospheric/plasmaspheric models, such as NeQuick, exhibit undesirable dependencies on the ionospheric peak height. As Prol and Hoque (2022) highlighted, these dependencies give rise to signatures associated with EIA crests at the plasmaspheric altitudes. In this context, the IRI-2001cor2 model appears more viable for integration with the plasmasphere. In the past, several models have been considered by IRI to describe the plasmasphere, including the Global Core Plasma Model (Gallagher et al., 2000), the IMAGE/RPI (Imager for Magnetopause – to – Aurora Global Exploration / Radio Plasma Imager) plasma-sphere model (Ozhogin et al., 2012), and the IZMIRAN model (Chasovitin et al., 1998; Gulyaeva and Titheridge, 2006). Based on earlier studies, IRI-2020 currently includes a plasmaspheric extension based on the merging between IRI-2001 family of topside models with the empirical plas-
<figure><img src="image_13.png" /><figcaption>Fig. 13. Ratios between IRI-modeled and GRACE-measured electron density values as a function of the Quasi-Dipole magnetic latitude (y-axis) and the day of the year (x-axis). The color represents the median value (in logarithmic scale) of the ratios inside each bin. Panel a) for IRI-2001, panel b) for IRI-2001cor, panel c) for IRI-2001cor2, and panel d) for IRI-NeQuick.</figcaption></figure>

masphere description provided by either the Gallagher
et al. (2000) or the Ozhogin et al. (2012) model. An alterna-
tive route to achieve a more accurate plasmaspheric extrap-
olation and reliable TEC estimations may be the
incorporation of new data sources in IRI, such as those
provided by the Van Allen Probes (Prol et al., 2022;
Hartley et al., 2023). It should be noted that the GNSS sig-
nals between satellites and receivers travel through several
regions above the topside ionosphere, each of them exhibit-
ing a complex and highly variable three-dimensional struc-
ture. Among these, the plasmasphere, which corotates with
the Earth and is located on closed geomagnetic field lines
connected to the mid-latitude ionosphere, can be reliably
modeled in three dimensions. However, at the plasma-
pause, which is the outer boundary of the plasmasphere,
electron density drops by approximately an order of mag-
nitude, while at higher altitudes the processes are vastly dif-
ferent from those inside the plasmasphere. Indeed, at
higher altitudes plasma particle motion is driven by magne-
tospheric convection and no longer corotate with the Earth
(Nishida, 1966). Accurate modeling of electron density in
this region still represents a challenge, and reproducing
realistic three-dimensional structures of different regions
of geospace up to GNSS altitudes remains an area of active
research.

**6. Conclusions and future developments**

This work investigated the performance of the IRI-2020
model in describing the topside ionosphere electron den-
sity variations through its four topside modeling options
by comparison with in-situ observations by GRACE,
ICON, and DMSP F15 LEO satellites. The dataset used
for validation covers two solar cycles (1999–2022) and
allowed investigating different local time, season, and solar
activity conditions, on a global basis and for the height
range 400–850 km. Albeit analyzing all the IRI-2020 top-
side options, the study mostly focused on the validation of
the performance of the newly introduced topside option,
IRI-2001cor2 (Bilitza and Xiong, 2021), which is the
default and recommended topside option in IRI-2020, in
comparison with the previous default option based on
the NeQuick topside model, IRI-NeQuick (Nava et al.,
2008). Our analysis evidenced both advantages and conse-
quences introduced with the IRI-2001cor2 model and
compared them with corresponding ones related to IRI-
NeQuick. Overall, both empirical models have room for
improvement which could be filled based on exploitation
of new datasets and/or different modeling techniques
and parameterizations. The main outcomes of the study
are:
<figure><img src="image_14.png" /><figcaption>Fig. 14. Same as Fig. 13 but for the DMSP F15 dataset.</figcaption></figure>

* IRI-2001cor2 model remarkably improved the description of the latitudinal variation of the topside electron density at low latitudes and for the LTs associated to the EIA phenomenology, accounting for the observed shift of EIA crests towards the geomagnetic equator with increasing altitude. The largest improvement by IRI-2001cor2 is for the lowest altitudes investigated by this study (400–600 km), while at the highest altitudes (830–850 km) it performs similar to IRI-NeQuick;

* IRI-2001cor2 model showed a solar activity trend at DMSP F15 altitude, thus signifying a solar activity variation not accounted for by the model. Moreover, the comparison at different QD latitudes evidenced that anchor points at low latitudes set latitudinal variations showing a relative maximum at the geomagnetic equator and relative minima at around ± 15° QD latitude, with sharp transitions between these latitudinal ranges;

* Overall, IRI-NeQuick model showed consistent performance at different altitudes but with the well-established issues connected to the representation of the low-latitude topside ionosphere. Due to the link between the bottomside and topside thickness parameters in the NeQuick formulation, the model shows latitudinal features associated to the F2-layer peak behavior also in the upper topside and in the plasmaspheric extension, which largely disagrees with observations.

The systematic work on the validation of the IRI-2020 topside options can be extended in several ways. First, there are a number of additional datasets that could be used to further enhance the data-model comparisons. For instance, the currently operating Swarm mission provides plasma density observations with very high fidelity during the daytime (e.g., Smirnov et al., 2021; Catapano et al., 2022; Xiong et al., 2022; Pignalberi et al., 2022c), and therefore could be utilized for the IRI validation. Furthermore, the *Communication and Navigation Outage Forecast System* (C/NOFS) mission provided very high-quality observations by means of the *Coupled Ion Neutral Dynamic Investigation* (CINDI) instrument, which covered different local times and altitudes along its orbit. These observations can also be included in future validation efforts. Amongst other datasets that provide a three-dimensional coverage of the topside ionosphere are the radio occultation observations by the COSMIC-1 and -2, GRACE and CHAMP missions, and these observations will be used to validate the IRI in a separate upcoming study. Moreover, the validation of the IRI topside options in connection with the plasmaspheric extensions also warrants separate investigations. There are several notable datasets that could be used for this task, including the in-situ Van Allen Probes data (Zhelavskaya et al., 2016), and historic observations by the RPI aboard the IMAGE mission (Reinisch et al., 2000).
## Data availability

The F10.7 observations are recorded at the Dominion Radio Astrophysical Observatory, and freely provided to the space weather community with support from Natural Resources Canada. F10.7 solar index data were downloaded through the OMNIWeb Data Explorer website (https://omniweb.gsfc.nasa.gov/form/dx1.html) maintained by the NASA. IRI Fortran code is available at the IRI website (http://irimodel.org/). GRACE data were obtained from the Information System and Data Center (ISDC) of GFZ German Research Centre for Geosciences at https://isdc.gfz-potsdam.de/homepage/. ICON data are available at https://icon.ssl.berkeley.edu/Data, and are also archived at the NASA Space Physics Data Facility (https://spdf.gsfc.nasa.gov), available through the Coordinated Data Analysis Web (CDAWeb) https://cdaweb.gsfc.nasa.gov/. DMSP F15 data were downloaded from the CEDAR Madrigal database at http://cedar.openmadrigal.org/.

## CRediT authorship contribution statement

**Alessio Pignalberi:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Dieter Bilitza:** Writing – review & editing, Writing – original draft, Validation, Software, Investigation, Conceptualization. **Pierdavide Coïsson:** Writing – review & editing, Validation, Investigation. **Haris Haralambous:** Writing – review & editing, Writing – original draft, Validation, Investigation. **Bruno Nava:** Writing – review & editing, Validation, Investigation, Conceptualization. **Michael Pezzopane:** Writing – review & editing, Validation, Supervision, Investigation, Conceptualization. **Fabricio Prol:** Writing – review & editing, Writing – original draft, Visualization, Validation, Investigation. **Artem Smirnov:** Writing – review & editing, Writing – original draft, Validation, Investigation. **David R. Themens:** Writing – review & editing, Writing – original draft, Visualization, Validation, Investigation, Formal analysis. **Chao Xiong:** Writing – review & editing, Investigation, Data curation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

The IRI team is acknowledged for developing and maintaining the IRI model and for giving access to the corresponding Fortran code via the IRI website at http://irimodel.org/. Haris Haralambous contribution was partially funded by the project "International Reference

Ionosphere Validation and Improvement" - IRIVM, (Ref. No:EXCELLENCE/0421/0422) that was co-funded by the Republic of Cyprus and the European Regional Development Fund (ERDF), in the frame of the Operational Programme "ΘΑΛΕΙΑ" 2021-2027 under Priority 1: "Competetive, Smart and Digital Economy" and the Specific Objective (1i): "Developing and enhancing research and innovation capacities and the uptake of advanced technologies". David R. Themens contribution to this work is supported in part through the United Kingdom Natural Environment Research Council (NERC) EISCAT3D: Fine-scale structuring, scintillation, and electrodynamics (FINESSE) (NE/W003147/1) and DRivers and Impacts of Ionospheric Variability with EISCAT-3D (DRIIVE) (NE/W003368/1) projects.

## References

Araujo-Pradere, E.A., Fuller-Rowell, T.J., Codrescu, M.V., 2002. STORM: An empirical storm-time ionospheric correction model 1. Model Description. Radio Science 37 (5), 1070. https://doi.org/10.1029/2001RS002467.

Balan, N., Liu, L.B., Le, H.J., 2018. A brief review of equatorial ionization anomaly and ionospheric irregularities. Earth Planet. Phys. 2 (4), 257-275. https://doi.org/10.26464/epp2018025.

Banks, P.M., 1969. The thermal structure of the ionosphere. Proceedings of the IEEE 57 (3), 258-281. https://doi.org/10.1109/PROC.1969.6959.

Bauer, S.J., 1969. Diffusive equilibrium in the topside ionosphere. Proceedings of the IEEE 57 (6), 1114-1118. https://doi.org/10.1109/PROC.1969.7163.

Bent, R. B., Llewellyn, S. K., Walloch, M. K., 1972. Description and evaluation of the Bent ionospheric model. Vol. I, Rep. SAMSO-TR-72-239. Available at https://apps.dtic.mil/sti/tr/pdf/AD0772733.pdf

Bilitza, D., 1985. Electron density in the equatorial topside. Adv. Space Res. 5 (10), 15-19. https://doi.org/10.1016/0273-1177(85)90174-7.

Bilitza, D., 2004. A correction for the IRI topside electron density model based on Alouette/ISIS topside sounder data. Adv. Space Res. 33 (6), 838-843. https://doi.org/10.1016/j.asr.2003.07.009.

Bilitza, D., 2009. Evaluation of the IRI-2007 model options for the topside electron density. Adv. Space Res. 44 (6), 701-706. https://doi.org/10.1016/j.asr.2009.04.036.

Bilitza, D., Williamson, R., 2000. Toward a better representation of the IRI topside based on ISIS and Alouette data. Adv. Space Res. 25 (1), 149-152. https://doi.org/10.1016/S0273-1177(99)00912-6.

Bilitza, D., Huang, X., Reinisch, B., Benson, R., Hills, H.K., Schar, W.B., 2004. Topside Ionogram Scaler With True Height Algorithm (TOPIST): Automated processing of ISIS topside ionograms. Radio Sci. 39, 1, RS1S27. https://doi.org/10.1029/2002RS002840.

Bilitza, D., Brown, S.A., Wang, M.Y., Souza, J.R., Roddy, P.A., 2012. Measurements and IRI model predictions during the recent solar minimum. Journal of Atmospheric and Solar-Terrestrial Physics 86, 99-106. https://doi.org/10.1016/j.jastp.2012.06.010.

Bilitza, D., Pezzopane, M., Truhlik, V., Altadill, D., Reinisch, B.W., Pignalberi, A., 2022. The International Reference Ionosphere model: a review and description of an ionospheric benchmark. Rev. Geophys. 60e2022RG000792. https://doi.org/10.1029/2022RG000792.

Bilitza, D., Xiong, C., 2021. A solar activity correction term for the IRI topside electron density model. Adv. Space Res. 68 (5), 2124-2137. https://doi.org/10.1016/j.asr.2020.11.012.

Bilitza, D., 1990. International Reference Ionosphere 1990. National Space Science Data Center, Report 90-22. Retrieved from https://irimodel.org/docs/IRI1990pp0-84.pdf
Booker, H.G., 1977. Fitting of multi-region ionospheric profiles of electron-density by a single analytic-function of height. J. Atmosph. Terrestr. Phys. 39 (5), 619–623. https://doi.org/10.1016/0021-9169(77) 90072-1.

Catapano, F., Buchert, S., Qamili, E., Nilsson, T., Bouffard, J., et al., 2022. Swarm Langmuir probes' data quality validation and future improvements. Geoscientific Instrumentation, Methods and Data Systems 11 (1), 149–162. https://doi.org/10.5194/gi-11-149-2022.

Chasovitin, Y.K., Gulyaeva, T.L., Deminov, M.G., Ivanova, S.E., 1998. Russian Standard Model of the Ionosphere (SMI). COST 251 Technical Document TD, 98(005), 161–172, Rutherford Appleton Laboratory, Oxford, UK.

Coïsson, P., Radicella, S.M., Nava, B., 2002. Comparisons of experimental topside electron concentration profiles with IRI and NeQuick models. Annals of Geophysics 45 (1), 111–116. https://doi.org/10.4401/ag-3492.

Coïsson, P., Radicella, S.M., 2004. The IRI topside parameters. Advances in Radio Science 2, 249–251. https://doi.org/10.5194/ars-2-249-2004.

Coïsson, P., Radicella, S.M., Leitinger, R., Nava, B., 2006. Topside electron density in IRI and NeQuick: Features and limitations. Adv. Space Res. 37 (5), 937–942. https://doi.org/10.1016/j.asr.2005.09.015.

Coïsson, P., Nava, B., Radicella, S.M., 2009. On the use of NeQuick topside option in IRI-2007. Adv. Space Res. 43 (11), 1688–1693. https://doi.org/10.1016/j.asr.2008.10.035.

European GNSS (Galileo) Open Service—Ionospheric Correction Algorithm for Galileo Single Frequency Users, Sep. 2016, European Commission, Brussels, Belgium, Sep. 2016. [Online]. Available: https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_ Ionospheric_Model.pdf

Ezquer, R.G., Jadur, C.A., Mosert de Gonzalez, M., 1998. IRI-95 TEC predictions for the South American peak of the equatorial anomaly. Adv. Space Res. 22 (6), 811–814. https://doi.org/10.1016/S0273-1177 (98)00103-3.

Fuller-Rowell, T.J., Araujo-Pradere, E., Codrescu, M.V., 2000. An empirical ionospheric storm-time correction model. Adv. Space Res. 25 (1), 139–146. https://doi.org/10.1016/S0273-1177(99)00911-4.

Gallagher, D.L., Craven, P.D., Comfort, R.H., 2000. Global core plasma model. Journal of Geophysical Research 105 (A8), 18819–18833. https://doi.org/10.1029/1999JA000241.

Garner, T.W., Taylor, B.T., Gaussiran, T.L., Coley, W.R., Hairston, M. R., Rich, F.J., 2010. Statistical behavior of the topside electron density as determined from DMSP observations: A probabilistic climatology. J. Geophys. Res. 115, A07306. https://doi.org/10.1029/2009JA014695.

Gulyaeva, T.L., Huang, X., Reinisch, B.W., 2002. The ionosphere-plasmasphere model software for ISO. Acta Geodaetica Et Geophysica Hungarica 37 (2–3), 143–152. https://doi.org/10.1556/ageod.37.2002. 2-3-3.

Gulyaeva, T.L., Titheridge, J.E., 2006. Advanced specification of electron density and temperature in the IRI ionosphere-plasmasphere model. Adv. Space Res. 38 (11), 2587–2595. https://doi.org/10.1016/j. asr.2005.08.045.

Haralambous, H., Oikonomou, C., 2013. Study of topside electron density profiles obtained by cosmic satellites and an ionosonde over Cyprus during a four year period. In *IEEE Geoscience and Remote Sensing Symposium (IGARSS) 2013* (pp. 3590–3593). https://doi.org/10.1109/ IGARSS.2013.6723606.

Hartley, D.P., Cunningham, G.S., Ripoll, J.-F., Malaspina, D.M., Kasahara, Y., Miyoshi, Y., et al., 2023. Using Van Allen Probes and Arase observations to develop an empirical plasma density model in the inner zone. J. Geophys. Res. Space Phys. 128e2022JA031012. https://doi.org/10.1029/2022JA031012.

Heelis, R.A., Stoneback, R.A., Perdue, M.D., et al., 2017. Ion Velocity Measurements for the Ionospheric Connections Explorer. Space Sci. Rev. 212, 615–629. https://doi.org/10.1007/s11214-017-0383-3.

Heelis, R.A., Depew, M.D., Chen, Y.J., et al., 2022. Ionospheric Connections (ICON) Ion Velocity Meter (IVM) Observations of the Equatorial Ionosphere at Solar Minimum. Space Sci Rev 218, 68. https://doi.org/10.1007/s11214-022-00936-w.

Hernández-Pajares, M., Garcia-Fernández, M., Rius, A., Notarpietro, R., von Engeln, A., Olivares-Pulido, G., Aragón-Ángel, Á., García-Rigo, A., 2017. Electron density extrapolation above F2 peak by the linear Vary-Chap model supporting new Global Navigation Satellite Systems-LEO occultation missions. J. Geophys. Res. Space Physics 122, 9003–9014. https://doi.org/10.1002/2017JA023876.

Hoque, M.M., Jakowski, N., 2012. Ionospheric propagation effects on GNSS signals and new correction approaches. In: Jin, S. (Ed.) *Global Navigation Satellite Systems*, IntechOpen, Rijeka, Croatia, pp. 381– 405. https://doi.org/10.5772/30090 (Chapter 16).

Huang, H., Moses, M., Volk, A.E., Elezz, O.A., Kassamba, A.A., Bilitza, D., 2021. Assessment of IRI-2016 hmF2 model options with digisonde, COSMIC observations for low and high solar flux conditions during 23rd solar cycle. Adv. Space Res. 68 (5), 2093–2103. https://doi.org/ 10.1016/j.asr.2021.01.033.

Hunsucker, R.D., 1991. Radio Techniques for Probing the Terrestrial Ionosphere. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978- 3-642-76257-4.

Immel, T.J., England, S.L., Mende, S.B., et al., 2018. The Ionospheric Connection Explorer Mission: Mission Goals and Design. Space Sci. Rev. 214, 13. https://doi.org/10.1007/s11214-017-0449-2.

ISO 16457, 2022. Space systems – Space Environment (natural and artificial) – The Earth’s ionosphere model: International reference ionosphere (IRI) model and extension to the plasmasphere. *International Standardization Organization*. Retrieved from http://www.iso. org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber= 61556.

Iwamoto, I., Katoh, H., Maruyama, T., Minakoshi, H., Watari, S., Igarashi, K., 2002. Latitudinal variations of solar flux dependence in the topside plasma density: Comparison between IRI model and observations. Adv. Space Res. 29 (6), 877–882. https://doi.org/ 10.1016/S0273-1177(02)00054-6.

Jones, W.B., Gallet, R.M., 1962. Representation of diurnal and geographical variations of ionospheric data by numerical methods. Journal of Research of the National Bureau of Standards, Section d: Radio Propagation 66 (4), 129–147. https://doi.org/10.6028/ jres.066D.043.

Jones, W.B., Gallet, R.M., 1965. Representation of diurnal and geographic variations of ionospheric data by numerical methods, II. Control of Instability. *ITU Telecommunication Journal* 32 (1), 18–28.

Jones, W.B., Graham, R.P., Leftin, M., 1969. Advances in ionospheric mapping by numerical methods. U.S. Department of Commerce, Boulder, Colorado, USA, ESSA Technical Report ERL 107-IT575.

Kashcheyev, A., Nava, B., 2019. Validation of NeQuick 2 model topside ionosphere and plasmasphere electron content using COSMIC POD TEC. J. Geophys. Res. Space Phys. 124, 9525–9536. https://doi.org/ 10.1029/2019JA026971.

Klenzing, J., Simoes, F., Ivanov, S., Heelis, R.A., Bilitza, D., Pfaff, R., Rowland, D., 2011. Topside equatorial ionospheric density and composition during and after extreme solar minimum. Journal of Geophysical Research 116 (A12), A12330. https://doi.org/10.1029/ 2011JA017213.

Klenzing, J., Simoes, F., Ivanov, S., Bilitza, D., Heelis, R.A., Rowland, D., 2013. Performance of the IRI-2007 model for equatorial topside ion density in the African sector for low and extremely low solar activity. Adv. Space Res. 52 (10), 1780–1790. https://doi.org/10.1016/j. asr.2012.09.030.

Klobuchar, J., 1987. Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans. Aerosp. Electron. Syst. AES-23, 3, 325–331. https://doi.org/10.1109/TAES.1987.310829.

Kutiev, I.S., Marinov, P.G., 2007. Topside sounder model of scale height and transition height characteristics of the ionosphere. Adv. Space Res. 39 (5), 759–766. https://doi.org/10.1016/j.asr.2006.06.013.

Kutiev, I.S., Marinov, P.G., Watanabe, S., 2006. Model of topside ionosphere scale height based on topside sounder data. Adv. Space Res. 37 (5), 943–950. https://doi.org/10.1016/j.asr.2005.11.021.
Laundal, K.M., Richmond, A.D., 2017. Magnetic Coordinate Systems. Space Sci. Rev. 206, 27–59. https://doi.org/10.1007/s11214-016-0275-y.

Leitinger, R., Nava, B., Hochegger, G., Radicella, S., 2001. Ionospheric profilers using data grids. Phys. Chem. Earth – Part c: Solar, Terr. Plan. Science 26 (5), 293–301. https://doi.org/10.1016/S1464-1917(01) 00002-2.

Liu, L., Wan, W., Zhang, M.-L., Ning, B., Zhang, S.-R., Holt, J.M., 2007a. Variations of topside ionospheric scale heights over Millstone Hill during the 30-day incoherent scatter radar experiment. Ann. Geophys. 25, 2019–2027. https://doi.org/10.5194/angeo-25-2019-2007.

Liu, L., Le, H., Wan, W., Sulzer, M.P., Lei, J., Zhang, M.-L., 2007b. An analysis of the scale heights in the lower topside ionosphere based on the Arecibo incoherent scatter radar measurements. J. Geophys. Res. 112, A06307. https://doi.org/10.1029/2007JA012250.

Lühr, H., Xiong, C., 2010. The IRI 2007 model overestimates electron density during the 23/24 solar minimum. Geophysical Research Letters 37 (23), L23101. https://doi.org/10.1029/2010GL045430.

Mengist, C.K., Yadav, S., Kotulak, K., Bahar, A., Zhang, S.-R., Seo, K.-H., 2020. Validation of International Reference Ionosphere model (IRI-2016) for F-region peak electron density height (hmF2): Comparison with incoherent scatter radar (ISR) and ionosonde measurements at Millstone Hill. Adv. Space Res. 65 (12), 2773–2781. https://doi.org/10.1016/j.asr.2020.03.017.

Migoya-Orue, Y.O., Radicella, S.M., Nava, B., 2013. Comparison of topside electron density computed by ionospheric models and plasma density observed by DMSP satellites. Adv. Space Res. 52 (10), 1710–1716. https://doi.org/10.1016/j.asr.2013.01.032.

Moses, M., Bilitza, D., Kumar Panda, S., Ochonugor, B.J., 2021. Assessment of IRI-2016 hmF2 model predictions with COSMIC observations over the African region. Adv. Space Res. 68 (5), 2115–2123. https://doi.org/10.1016/j.asr.2020.10.029.

Nava, B., Coïsson, P., Radicella, S., 2008. A new version of the NeQuick ionosphere electron density model. J. Atmos. Solar-Terr. Phys. 70 (15), 1856–1862. https://doi.org/10.1016/j.jastp.2008.01.015.

Nishida, A., 1966. Formation of plasmapause, or magnetospheric plasma knee, by the combined action of magnetospheric convection and plasma escape from the tail. Journal of Geophysical Research 71 (23), 5669–5679. https://doi.org/10.1029/2012RS004989.

Nsumei, P., Reinisch, B.W., Huang, X., Bilitza, D., 2012. New Vary-Chap profile of the topside ionosphere electron density distribution for use with the IRI model and the GIRO real time data. Radio Science 47, RS0L16. https://doi.org/10.1029/2012RS004989.

Olivares-Pulido, G., Hernández-Pajares, M., Aragón-Ángel, A., Garcia-Rigo, A., 2016. A linear scale height chapman model supported by GNSS occultation measurements. J. Geophys. Res. Space Phys. 121, 7932–7940. https://doi.org/10.1002/2016JA022337.

Oyama, K.I., Balan, N., Watanabe, S., Takahashi, T., Isoda, F., Bailey, G.J., Oya, H., 1996. Morning overshoot of Te enhanced by downward plasma drift in the equatorial topside ionosphere. J. Geomagn. Geoelectr. 48, 959–966. https://doi.org/10.5636/jgg.48.959.

Ozhogin, P., Tu, J., Song, P., Reinisch, B.W., 2012. Field-aligned distribution of the plasmaspheric electron density: An empirical model derived from the IMAGE RPI measurements. Journal of Geophysical Research 117 (A6). https://doi.org/10.1029/2011JA017330.

Pezzopane, M., Pignalberi, A., 2019. The ESA Swarm mission to help ionospheric modeling: a new NeQuick topside formulation for mid-latitude regions. Sci. Rep. 9, 12253. https://doi.org/10.1038/s41598-019-48440-6.

Pezzopane, M., Pignalberi, A., Nava, B., 2023. On the low-latitude NeQuick topside ionosphere mismodelling: The role of parameters H₀, g, and r. Adv. Space Res. 72 (4), 1224–1236. https://doi.org/10.1016/j.asr.2023.04.014.

Pignalberi, A., Pezzopane, M., Tozzi, R., De Michelis, P., Coco, I., 2016. Comparison between IRI and preliminary Swarm Langmuir probe measurements during the St. Patrick Storm Period. *Earth Planets Sp.* 68, 93. https://doi.org/10.1186/s40623-016-0466-5.

Pignalberi, A., Pezzopane, M., Rizzi, R., 2018. Modeling the lower part of the topside ionospheric vertical electron density profile over the

European region by means of Swarm satellites data and IRI UP method. Space Weather 16, 304–320. https://doi.org/10.1002/2017SW001790.

Pignalberi, A., Pezzopane, M., Nava, B., Coïsson, P., 2020a. On the link between the topside ionospheric effective scale height and the plasma ambipolar diffusion, theory and preliminary results. Sci. Rep. 10, 17541. https://doi.org/10.1038/s41598-020-73886-4.

Pignalberi, A., Pezzopane, M., Themens, D.R., Haralambous, H., Nava, B., Coïsson, P., 2020b. On the Analytical Description of the Topside Ionosphere by NeQuick: Modeling the Scale Height Through COSMIC/FORMOSAT-3 Selected Data. *IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.* 13, 1867–1878. https://doi.org/10.1109/JSTARS.2020.2986683.

Pignalberi, A., Pietrella, M., Pezzopane, M., 2021. Towards a Real-Time Description of the Ionosphere: A Comparison between International Reference Ionosphere (IRI) and IRI Real-Time Assimilative Mapping (IRTAM) Models. Atmosphere 12, 1003. https://doi.org/10.3390/atmos12081003.

Pignalberi, A., Pezzopane, M., Nava, B., 2022a. Optimizing the NeQuick topside scale height parameters through COSMIC/FORMOSAT-3 radio occultation data. IEEE Geosc. Rem. Sens. Lett. 19, 1–5. https://doi.org/10.1109/LGRS.2021.3096657.

Pignalberi, A., Pietrella, M., Pezzopane, M., Nava, B., Cesaroni, C., 2022b. The Ionospheric Equivalent Slab Thickness: A Review Supported by a Global Climatological Study Over Two Solar Cycles. Space Science Reviews 218, 37. https://doi.org/10.1007/s11214-022-00909-z.

Pignalberi, A., Pezzopane, M., Coco, I., Piersanti, M., Giannattasio, F., De Michelis, P., Tozzi, R., Consolini, G., 2022c. Inter-Calibration and Statistical Validation of Topside Ionosphere Electron Density Observations Made by CSES—01 Mission. Remote Sens. 14, 4679. https://doi.org/10.3390/rs14184679.

Pignalberi, A., Pezzopane, M., Alberti, T., Coco, I., Consolini, G., D'Angelo, G., De Michelis, P., Giannattasio, F., Nava, B., Piersanti, M., Tozzi, R., 2023. Modeling the Topside Ionosphere Effective Scale Height through In Situ Electron Density Observations by Low-Earth-Orbit Satellites. Universe 9, 280. https://doi.org/10.3390/universe9060280.

Pignalberi, A., Nava, B., Pietrella, M., Pezzopane, M., Coïsson, P., Cesaroni, C., 2024. Ionospheric equivalent slab thickness ingestion into the NeQuick model. Annals of Geophysics 66 (PA528) https://www.annalsofgeophysics.eu/index.php/annals/article/view/9026.

Prol, F.S., Hernandez-Pajares, M., Camargo, P.O., Muella, M.T.A.H., 2018. Spatial and temporal features of the topside ionospheric electron density by a new model based on GPS radio occultation data. J. Geophys. Res. Space. Phys. 123, 2104–2115. https://doi.org/10.1002/2017JA024936.

Prol, F.S., Hoque, M.M., 2022. A Tomographic Method for the Reconstruction of the Plasmasphere Based on COSMIC/ FORMOSAT-3 Data. *IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.* 15, 2197–2208. https://doi.org/10.1109/JSTARS.2022.3155926.

Prol, F.S., Themens, D., Hernández-Pajares, M., Camargo, P.O., Muella, M.T.A.H., 2019. Linear vary-chap topside electron density model with topside sounder and radio-occultation data. Surv. Geophys. 40, 277–293. https://doi.org/10.1007/s10712-019-09521-3.

Prol, F.S., Smirnov, A.G., Hoque, M.M., Shprits, Y.Y., 2022. Combined model of topside ionosphere and plasmasphere derived from radio-occultation and Van Allen Probes data. Sci. Rep. 12, 9732. https://doi.org/10.1038/s41598-022-13302-1.

Radicella, S.M., Leitinger, R., 2001. The evolution of the DGR approach to model electron density profiles. Adv. Space Res. 27 (1), 35–40. https://doi.org/10.1016/S0273-1177(00)00138-1.

Ratcliffe, J.A., 1972. An introduction to the ionosphere and magnetosphere. Cambridge University Press, Cambridge, UK.

Rawer, K., 1963. Propagation of decimeter waves (HF band). In: Landmark, B. (Ed.), Meteorological and Astronomical Influences on
Radio Wave Propagation. Academic Press, Cambridge, MA, USA, pp. 221–250.

Rawer, K., 1984. Modelling of neutral and ionized atmospheres. In *Encyclopedia of physics, XLIX/7*. Springer, Berlin, Heidelberg, pp. 223–533.

Rawer, K., Bilitza, D., Ramakrishnan, S., Sheikh, N., 1978a. Intentions and build-up of the International reference Ionosphere. In *Operational modelling of the aerospace propagation environment. AGARD Conference Proceedings No. 238* (pp. 6.1–6.9), Paris, France.

Rawer, K., Bilitza, D., Ramakrishnan, S., 1978b. International reference ionosphere 78. Special Report, International Union of Radio Science (URSI), Bruxelles, Belgium.

Reinisch, B., Haines, D., Bibl, K., et al., 2000. The Radio Plasma Imager investigation on the IMAGE spacecraft. Space Science Reviews 91, 319–359. https://doi.org/10.1023/A:1005252602159.

Reinisch, B.W., Nsumei, P., Huang, X., Bilitza, D.K., 2007. Modeling the F2 topside and plasmasphere for IRI using IMAGE/RPI and ISIS data. Adv. Space Res. 39 (5), 731–738. https://doi.org/10.1016/j.asr.2006.05.032.

Rich, F.J., 1994. Users Guide for the Topside Ionospheric Plasma Monitor (SSIES, SSIES-2 and SSIES-3) on Spacecraft of the Defense Meteorological Satellite Program, Volume 1: Technical Description. PL-TR-94-2187 Environmental Research Papers, No. 1151. Phillips laboratory, Directorate of geophysics, Air Force Materiel Command Hanscom AFB, MA, 01731-3010, USA. Available at https://apps.dtic.mil/sti/pdfs/ADA315731.pdf

Rishbeth, H., Garriott, O., 1969. Introduction to Ionospheric Physics, International Geophysics Series, Vol. 14. Academic Press, New York, NY, USA.

Rush, C.M., Fox, M., Bilitza, D., Davies, K., McNamara, L., Stewart, F. G., PoKempner, M., 1989. Ionospheric mapping-an update of foF2 coefficients. Telecommun. J. 56, 179–182.

Schunk, R.W., Nagy, A.F., 1978. Electron temperatures in the F region of the ionosphere: Theory and observations. Rev. Geophys. 16 (3), 355–399. https://doi.org/10.1029/RG016i003p00355.

Scotto, C., Sabbagh, D., Ippolito, A., 2023. Accuracy of hmF2 estimations, including IRI-2020 options and ionograms validated parameters, compared to ISR measurements at Millstone Hill. Adv. Space Res. 72 (8), 3202–3211. https://doi.org/10.1016/j.asr.2023.07.012.

Shaikh, M.M., Nava, B., Haralambous, H., 2018. On the use of topside RO-derived electron density for model validation. J. Geophys. Res. Space. Phys. 123, 3943–3954. https://doi.org/10.1029/2017JA025132.

Shim, J.S., Kuznetsova, M., Rastätter, L., Hesse, M., Bilitza, D., Codrescu, M., Emery, B.A., Foster, B., Fuller-Rowell, T., Huba, J., Mannucci, A.J., Ridley, A., Scherliess, L., Schunk, R.W., Stephens, P., Thompson, D.C., Zhu, L., Anderson, D., Chau, J.L., Sojka, J.J., Rideout, B., 2011. CEDAR Electrodynamics Thermosphere Ionosphere 1 (ETI) Challenge for Systematic Assessment of Ionosphere/Thermosphere Models 1: NmF2, hmF2, and Vertical Drift Using Ground Based Observations. Space Weather 9 (12), S12003. https://doi.org/10.1029/2011SW000727.

Shim, J.S., Kuznetsova, M., Rastätter, L., Hesse, M., Bilitza, D., Butala, M., Codrescu, M., Emery, B.A., Foster, B., Fuller-Rowell, T.J., Huba, J., Mannucci, A.J., Pi, X., Ridley, A., Scherliess, L., Schunk, R.W., Sojka, J.J., Stephens, P., Thompson, D.C., Weimer, D., Zhu, L., Sutton, E., 2012. CEDAR Electrodynamics Thermosphere Ionosphere (ETI) Challenge for systematic assessment of ionosphere/thermosphere models: Electron density, neutral density, NmF2, and hmF2 using space based observations. Space Weather 10 (10), S10004. https://doi.org/10.1029/2012SW000851.

Shim, J.S., Rastätter, L., Kuznetsova, M., Bilitza, D., Codrescu, M., Coster, A.J., Emery, B.A., Fedrizzi, M., Förster, M., Fuller-Rowell, T. J., Gardner, L.C., Goncharenko, L., Huba, J., McDonald, S.E., Mannucci, A.J., Namgaladze, A.A., Pi, X., Prokhorov, B.E., Ridley, A.J., Scherliess, L., Schunk, R.W., Sojka, J.J., Zhu, L., 2017. CEDAR-GEM challenge for systematic assessment of Ionosphere/thermosphere models in predicting TEC during the 2006 December storm event.

Space Weather 15 (10), 1238–1256. https://doi.org/10.1002/2017SW001649.

Shim, J.S., Tsagouri, I., Goncharenko, L., Rastaetter, L., Kuznetsova, M., Bilitza, D., Codrescu, M., Coster, A.J., Solomon, S.C., Fedrizzi, M., Förster, M., Fuller-Rowell, T.J., Gardner, L.C., Huba, J., Namgaladze, A.A., Prokhorov, B.E., Ridley, A.J., Scherliess, L., Schunk, R. W., Sojka, J.J., Zhu, L., 2018. Validation of ionospheric specifications during geomagnetic storms: TEC and foF2 during the 2013 March storm event. Space Weather 16 (11), 1686–1701. https://doi.org/10.1029/2018SW002034.

Subbin, V.N., 2015. Global median model of the F2-layer peak height based on ionospheric radio-occultation and ground based digisonde observations. Adv. Space Res. 56, 916–928. https://doi.org/10.1016/j.asr.2015.05.029.

Singh, A.K., Haralambous, H., Oikonomou, C., 2021. Validation and improvement of NeQuick topside ionospheric formulation using COSMIC/FORMOSAT-3 data. J. Geophys. Res. Space. Phys. 126e2020JA028720. https://doi.org/10.1029/2020JA028720.

Smirnov, A., Shprits, Y., Zhelavskaya, I., Lühr, H., Xiong, C., Goss, A., et al., 2021. Intercalibration of the plasma density measurements in Earth's topside ionosphere. J. Geophys. Res. Space. Phys. 126e2021JA029334. https://doi.org/10.1029/2021JA029334.

Smirnov, A., Shprits, Y., Prol, F., et al., 2023. A novel neural network model of Earth's topside ionosphere. Sci Rep 1303. https://doi.org/10.1038/s41598-023-28034-z.

Stankov, S.M., Jakowski, N., Heise, S., Muhtarov, P., Kutiev, I., Warnat, R., 2003. A new method for reconstruction of the vertical electron density distribution in the upper ionosphere and plasmasphere. Journal of Geophysical Research 108 (A5), 1164. https://doi.org/10.1029/2002JA009570.

Stankov, S.M., Jakowski, N., 2006. Topside ionospheric scale height analysis and modelling based on radio occultation measurements. Journal of Atmospheric and Solar - Terrestrial Physics 68 (2), 134–162. https://doi.org/10.1016/j.jastp.2005.10.003.

Stolle, C., Liu, H., Truhlík, V., Lühr, H., Richards, P.G., 2011. Solar flux variation of the electron temperature morning overshoot in the equatorial *F* region. J. Geophys. Res. 116, A04308. https://doi.org/10.1029/2010JA016235.

Tapley, B.D., Bettadpur, S., Watkins, M., Reigber, C., 2004. The gravity recovery and climate experiment: mission overview and early results. Geophys. Res. Lett. 31, L09607. https://doi.org/10.1029/2004GL019920.

Tapping, K.F., 2013. The 10.7 cm solar radio flux (F10.7). Space Weather 11, 394–406. https://doi.org/10.1002/swe.20064.

Themens, D.R., Jayachandran, P.T., Nicolls, M.J., MacDougall, J.W., 2014. A top to bottom evaluation of IRI 2007 within the polar cap. J. Geophys. Res. Space Physics 119, 6689–6703. https://doi.org/10.1002/2014JA020052.

Themens, D.R., Jayachandran, P.T., 2016. Solar Activity Variability in the IRI at high latitudes: Comparisons with GPS Total Electron Content. J. Geophys. Res. Space Physics 121, 3793–3807. https://doi.org/10.1002/2016JA022664.

Themens, D.R., Jayachandran, P.T., Galkin, I., Hall, C., 2017. The Empirical Canadian High Arctic Ionospheric Model (E-CHAIM): NmF2 and hmF2. J. Geophys. Res. Space Physics 122, 9015–9031. https://doi.org/10.1002/2017JA024398.

Themens, D.R., Jayachandran, P.T., Bilitza, D., Erickson, P.J., Häggström, I., Lyashenko, M.V., Reid, B., Varney, R.H., Pustovalova, L., 2018. Topside electron density representations for middle and high latitudes: A topside parameterization for E-CHAIM based on the NeQuick. J. Geophys. Res. Space. Phys. 123, 1603–1617. https://doi.org/10.1002/2017JA024817.

Themens, D.R., Jayachandran, P.T., McCaffrey, A.M., 2019a. Validating the performance of the Empirical Canadian High Arctic Ionospheric Model (E-CHAIM) with in situ observations from DMSP and CHAMP. J. Space Weather and Space Clim. 9, A21. https://doi.org/10.1051/swsc/2019021.
Themens, D.R., Jayachandran, P.T., McCaffrey, A.M., Reid, B., Varney, R.H., 2019b. A bottomside parameterization for the Empirical Canadian High Arctic Ionospheric Model (E-CHAIM). Radio Sci. 54, 397-414. https://doi.org/10.1029/2018RS006748.

Themens, D.R., Reid, B., Jayachandran, P.T., Larson, B., Koustov, A.V., Elvidge, S., McCaffrey, A.M., Watson, C.J., 2021. E-CHAIM as a model of Total Electron Content: Performance and Diagnostics. Space Weather 19e2021SW002872. https://doi.org/10.1029/2021SW002872.

Titheridge, J.E., 1976. Ion transition heights from topside electron density profiles. Planet. Space Sci. 24, 229-246. https://doi.org/10.1016/0032-0633(76)90020-9.

Trísková, L., Truhlik, V., Šmilauer, J., 2002. On possible improvements of outer ionosphere ion composition model in IRI. Adv. Space Res. 29 (6), 849-858. https://doi.org/10.1016/S0273-1177(02)00041-8.

Tulasi Ram, S., Su, S.-Y., Liu, C.H., Reinisch, B.W., McKinnell, L.-A., 2009. Topside ionospheric effective scale height (HT) derived with ROCSAT-1 and ground-based ionosonde observations at equatorial and midlatitude stations. Journal of Geophysical Research 114, A10309. https://doi.org/10.1029/2009JA014485.

Vaishnav, R., Jin, Y., Golam Mostafa, M., Aziz, S.R., Zhang, S.-R., Jacobi, C., 2021. Study of the upper transition height using ISR observations and IRI predictions over Arecibo. Adv. Space Res. 68 (5), 2177-2185. https://doi.org/10.1016/j.asr.2020.10.010.

Wang, S., Huang, S., Fang, H., 2015. Topside ionospheric VARY-chap scale height retrieved from the COSMIC/FORMOSAT-3 data at midlatitudes. Adv. Space Res. 56 (5), 893-899. https://doi.org/10.1016/j.asr.2015.04.021.

Wu, M.J., Guo, P., Fu, N.F., Xu, T.L., Xu, X.S., Jin, H.L., Hu, X.G., 2016. Topside correction of IRI by global modeling of ionospheric scale height using COSMIC radio occultation data. J. Geophys. Res. Space Phys. 121, 5675-5692. https://doi.org/10.1002/2016JA022785.

Wu, Y.J.J., Mende, S., Harding, B.J., et al., 2023. Cross-Validation of the Ionospheric Vertical Drift Measurements Based on ICON/IVM, Swarm, and the Ground-Based Radar at the Jicamarca Radio Observatory. Space Sci Rev 219, 47. https://doi.org/10.1007/s11214-023-00993-9.

Xiong, C., Lühr, H., Stolle, C., 2021. GRACE Electron Density of the K-Band Ranging System (KBR). V. 0101. GFZ Data Services. https://doi.org/10.5880/GFZ.2.3.2021.003

Xiong, C., Park, J., Lühr, H., Stolle, C., Ma, S.Y., 2010. Comparing plasma bubble occurrence rates at CHAMP and GRACE altitudes during high and low solar activity. Ann. Geophys. 28, 1647-1658. https://doi.org/10.5194/angeo-28-1647-2010.

Xiong, C., Lühr, H., Ma, S., Schlegel, K., 2015. Validation of GRACE electron densities by incoherent scatter radar data and estimation of plasma scale height in the topside ionosphere. Adv. Space Res. 55 (8), 2048-2057. https://doi.org/10.1016/j.asr.2014.07.022.

Xiong, C., Jiang, H., Yan, R., Lühr, H., Stolle, C., Yin, F., et al., 2022. Solar flux influence on the in-situ plasma density at topside ionosphere measured by Swarm satellites. J. Geophys. Res. Space Phys. 127e2022JA030275. https://doi.org/10.1029/2022JA030275.

Zhelavskaya, I.S., Spasojevic, M., Shprits, Y.Y., Kurth, W.S., 2016. Automated determination of electron density from electric field measurements on the Van Allen Probes spacecraft. J. Geophys. Res. Space Phys. 121 (5), 4611-4625. https://doi.org/10.1002/2015JA022132.

Zhu, J., Zhao, B., Wan, W., Ning, B., Zhang, S., 2015. A new topside profiler based on Alouette/ISIS topside sounding. Adv. Space Res. 5 (10), 2080-2090. https://doi.org/10.1016/j.asr.2015.08.008.

Zolesi, B., Cander, L., 2014. Ionospheric prediction and forecasting. Springer, Berlin, Heidelberg.