# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL110559

**Key Points:**

* Total square-Root Electron Content (TREC) is a new measure of the ionospheric electron content for electromagnetic signals in the ELF band

* A method to retrieve TREC from fractional-hop whistlers in the ELF detected by the ESA Swarm mission is proposed

* The method is validated using TREC computed with independently constrained electron density profiles close to the Swarm whistler locations

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

M. Jenner and P. Coïsson,
jenner@ipgp.fr; coisson@ipgp.fr

**Citation:**

Jenner, M., Coïsson, P., Hulot, G., Buresova, D., Truhlik, V., & Chauvet, L. (2024). Total root electron content: A new metric for the ionosphere below low Earth orbiting satellites. *Geophysical Research Letters*, *51*, e2024GL110559. https://doi.org/10.1029/2024GL110559

Received 31 MAY 2024

Accepted 24 JUL 2024

© 2024. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<figure><img src="image_1.png" /></figure>

## Total Root Electron Content: A New Metric for the Ionosphere Below Low Earth Orbiting Satellites

M. Jenner¹ ID, P. Coïsson¹ ID, G. Hulot¹ ID, D. Buresova² ID, V. Truhlik² ID, and L. Chauvet¹ ID

¹Université Paris Cité, Institut de physique du globe de Paris, CNRS, Paris, France, ²Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czechia

**Abstract** Powerful lightning strikes generate broadband electromagnetic signals. At Extremely Low Frequencies (ELF), the signal partly leaks into the ionosphere and produces whistlers that can be detected by satellites. Indeed, the satellites of the European Space Agency (ESA) Swarm Earth Explorer mission can detect those signals during 250 Hz burst-mode acquisition campaigns of their Absolute Scalar Magnetometers (ASM). The dispersion of these whistlers depends on their propagation path and the distribution of ionization in the ionosphere crossed along that path. In this paper, we introduce a technique to derive a new measure of ionosphere electron content, the Total square-Root Electron Content (TREC), using the arrival times of two frequencies of the whistler signal. We validate this approach by using data from ionosondes and from in situ measurements of the electron density at Swarm location. This technique brings new opportunities for sounding the ionosphere in regions poorly observed by other techniques.

**Plain Language Summary** A lightning strike generates an electromagnetic impulse that propagates within Earth's atmosphere and eventually leaks out into the ionosphere. As it propagates through the ionosphere toward low-Earth orbiting (LEO) satellites, it gets converted into a so-called whistler, with high frequencies arriving earlier than low frequencies. This frequency dispersion depends on the state of the ionosphere. Here, we analyse such whistler waves detected by magnetometers onboard the European Space Agency Swarm satellites to recover information about the state of the ionosphere below the satellites. We first introduce a new metric, the Total Root Electron Content (TREC), which quantifies the cumulative value of the square root of electron density along the path of the whistler. We next propose a method to recover the TREC from the analysis of the whistler dispersion. We finally validate this method by using independently derived ionospheric electron density profiles to infer expected TREC values. Our results show that whistlers detected by LEO satellites can be used to locally improve the widely used empirical International Reference Ionosphere model. Such whistler inferred TREC values could be used to sound the ionosphere above places difficult to sample with conventional measuring techniques, and help better model and understand the highly dynamic ionosphere.

## 1. Introduction

Most of the remote sensing techniques of the ionosphere rely heavily on ground instruments and infrastructures, for example, GNSS receivers (Jin et al., 2014), Ionosondes, Incoherent Scatter Radars, sounding rockets (Hunsucker, 1991; Schunk & Nagy, 2009). This limits the geographic coverage of the available measurements, especially above oceans and remote parts of the globe. Space-born sounding techniques can help fill the gaps. In the present work we introduce a novel technique relying on the detection of natural electromagnetic signals detected by the satellites of the ESA Swarm mission to sound the ionosphere below them.

The primary goal of the Swarm mission is to recover the many components of the Earth's magnetic field and monitor their evolution (Friis-Christensen et al., 2006). Each of the three Swarm satellites is equipped with a high-precision magnetometry payload consisting of a Vector Flux-gate Magnetometer (VFM), a set of three star cameras for attitude restitution, and an Absolute Scalar Magnetometer (ASM) to provide absolute scalar data and calibrate the VFM. These ASM instruments can further provide either 1 Hz self-calibrated vector field components, when operated in “vector mode,” or 250 Hz scalar field values, when operated in “burst mode” (Léger et al., 2015). Both these mutually exclusive modes have been tested with success early on in the mission (Fratter et al., 2016). For some years, only the vector mode was operated, leading to the demonstration that ASM instruments could indeed single-handedly provide high-quality calibrated vector field components for global magnetic modeling purposes (Hulot et al., 2015; Vigneron et al., 2015, 2021). More recently, however, the
discovery of large numbers of Extremely Low Frequency (ELF) lightning-generated whistlers (whistlers for short) in early burst mode session data led to a change in the operation strategy of the ASM instruments. Burst mode sessions are now operated regularly on two of the Swarm satellites to provide extensive opportunities to investigate such whistlers in the ELF band.

This wave phenomenon was extensively studied in the Very Low Frequency (VLF) band in both the ionosphere and the magnetosphere (Budden, 1985; Davies, 1989; Ferencz et al., 2001; Hellwell, 1965; Stix, 1992; Storey, 1953; Swanson, 2003) but remains poorly described and investigated in the lower and intermediate part of the ELF band between 3 Hz and 1 kHz (Barr et al., 2000). Whistlers originate from the broadband electromagnetic impulse caused by lightning strikes in the lower atmosphere (Chum et al., 2006; Némec et al., 2010; Parrot et al., 2019; Shklyar & Kuzichev, 2014). The signal travels in the Earth-ionosphere wave-guide and eventually leaks out into the ionosphere where the signal propagates in the whistler mode. The ionosphere is a dispersive medium and thus, the propagation velocity depends on both the frequency and the state of ionization of the traversed layers. This is the reason of the characteristic whistling shape of whistlers. Several studies (Carpenter & Smith, 1964; Lichtenberger, 2009; Park, 1972) take advantage of this property to measure magnetospheric electron density from ground-detected whistlers.

Remote sensing of the ionosphere using its electromagnetic dispersive properties is already classically achieved with GNSS signals by using the difference in propagation time of two different frequencies in the Ultra High Frequency band. This allows the retrieval of the Total Electron Content (TEC) along the signal propagation path, generally approximated by a straight line from the satellite to the receiver (Jin et al., 2014; Klobuchar, 1987; Leitinger et al., 1984). In the present work, we propose an analogous approach taking advantage of natural whistler signals detected in orbit in the ELF band. As we will show, this approach allows the recovery of the square-root of the electron density integrated along the signal propagation path, from its ionospheric entry point to the satellite, here slightly bent through the influence of the Earth's magnetic field. We call this quantity the Total square-Root Electron Content (TREC).

In what follows, we first develop a theoretical approach of ionospheric propagation of whistler wave in the ELF to draw a link between the group delay of specific frequencies of the whistler and the TREC (Section 2.1). We next introduce a method to extract the TREC from the group delay of two chosen frequencies (Section 2.2). To illustrate and test the method, we rely on whistlers detected by the Swarm ASMs and choose events located nearby active ionosonde stations so as to access an independent source of measurements of the ionospheric plasma density (Section 3). The method is then validated by comparing TREC independently derived from the latter to TREC derived from whistlers (Section 4). After discussing these results (Section 5), we finally conclude by highlighting the potential of such whistler-derived TREC to help constrain the state of the ionosphere (Section 6).

## 2. Methodology

### 2.1. Propagation of ELF Signals in the Earth Ionosphere

The dispersion of electromagnetic waves in a dispersive medium can directly be inferred from the knowledge of its refractive index *n* as a function of the wave frequency. Here we derive a workable approximation of *n* within hypotheses stemming from the characteristics of the ionospheric medium and signals in the ELF band.

#### 2.1.1. Hypotheses

The following developments are made under hypotheses compatible with whistler signals propagating through a stratified ionosphere from the base of the E region (~90 km) to the altitude of the highest Swarm satellite (~510 km). It is composed of a cold and collision-less plasma of electrons and atomic oxygen ions in equal part, assuming quasi-neutrality ($N_e = N_i = N$). This is reasonable since oxygen is the dominant species in most of the altitude range of Swarm observations. For this work, we assume the plasma density has spherical symmetry. Since we study signals detected by the Swarm ASMs, we concentrate on the propagation within the frequency band sensed by this instrument, between 10 and 120 Hz, corresponding roughly to wavelength between 1 and 100 km in the ionosphere. When studying propagation in a plasma it is useful to make use of following frequencies:
$$f_{pe}^2 = \frac{Ne^2}{4\pi^2\epsilon_0 m_e} = \alpha N \qquad f_{pi}^2 = \frac{f_{pe}^2}{\mu}$$

$$f_{ge} = \frac{eB}{2\pi m_e} = \beta B \qquad f_{gi} = \frac{f_{ge}}{\mu}$$

with:

$$\mu = \frac{m_i}{m_e} = \frac{f_{pe}^2}{f_{pi}^2} = \frac{f_{ge}}{f_{gi}}$$

$e$ being the electron charge, $m_e$ the electron mass, $m_i$ the ion mass and $\epsilon_0$ the vacuum permittivity. $f_{pe}$ and $f_{pi}$ are the electron and oxygen ion plasma frequencies (respectively ~1 MHz and ~10 kHz) and $f_{ge}$ and $f_{gi}$ are the electron (~0.1 MHz) and oxygen ion gyrofrequencies (~20 to ~50 Hz). These frequencies are singularities for ionospheric propagation (Stix, 1992, chapter 2). Only $f_{gi}$ lies within the ASM band and to address this issue we chose to limit this study to frequencies $f > f_{gi}$.

### 2.1.2. Stix Refractive Index Equation

A whistler wave, at frequency $f$ propagating in the ionosphere with the angle $\psi$ with respect to the geomagnetic field $\vec{B}$, follows the refractive index equation reported by Stix (1992, equations 1.34 and 1.35, page 9), which in general includes two modes. In the present context, the only mode that allows propagation corresponds to:

$$n^2 = \frac{RL \sin^2 \psi + PS(1 + \cos^2 \psi) - \sqrt{(RL - PS)^2 \sin^4 \psi + 4P^2 D^2 \cos^2 \psi}}{2S \sin^2 \psi + 2P \cos^2 \psi} \quad (1)$$

where $R, L, P, S, D$ are defined as:

$$\begin{align*}
R &= 1 - \frac{X}{1 - Y} - \frac{X}{\mu + Y} \\
L &= 1 - \frac{X}{1 + Y} - \frac{X}{\mu - Y} \\
P &= 1 - X \left(1 + \frac{1}{\mu}\right) \tag{2} \\
S &= \frac{1}{2}(R + L) \\
D &= \frac{1}{2}(R - L)
\end{align*}$$

with:

$$X = \frac{f_{pe}^2}{f^2}$$

$$Y = \frac{f_{ge}}{f}$$

In the studied region of the ionosphere, typical plasma density $N$ varies between $1 \times 10^9 \text{ m}^{-3}$ and $1 \times 10^{12} \text{ m}^{-3}$ within an ambient magnetic field $B$ of ~30,000 nT. In these conditions, in the band of interest ($f_{gi} < f < 120$ Hz):

$$X \gg Y \quad Y \gg 1$$
$$X \gg \mu \quad X \gg Y^2/\mu$$

R, L, P, S, D then become:

$$ 
\begin{aligned}
R &= \frac{\mu X}{Y(Y + \mu)} \\
L &= \frac{\mu X}{Y(Y - \mu)} \\
P &= -X \\
S &= \frac{\mu X}{Y^2 - \mu^2} \\
D &= \frac{-\mu S}{Y}
\end{aligned} 
\qquad (3) $$

Numerical estimates of the ratios RL/PS and P/S (see Figure S1 in Supporting Information S1) show that, in the ASM band:

$$ \left| \frac{RL}{PS} \right| \ll 1 \qquad (4) $$

Also, as shown in Figure S1 in Supporting Information S1, when $f > f_{gi} + 10$ Hz and $|\psi - 90^\circ| > 1^\circ$:

$$ |S \sin^2 \psi| \ll |P \cos^2 \psi| \qquad (5) $$

With these approximations we can simplify the refractive index in the ELF band (details in Equation S1 in Supporting Information S1):

$$ n^2 = S \left( 1 + \frac{1}{2} \tan^2 \psi - \sqrt{\frac{1}{4} \tan^4 \psi + \frac{\mu^2}{Y^2 \cos^2 \psi}} \right) \qquad (6) $$

This equation is equivalent to what Booker and Dyce (1965, equation 27) call the hydromagnetic approximation. For ease of manipulation in the following derivation, we introduce $M(f, B, \psi)$ so that:

$$ n^2 = S(f, B, N)M(f, B, \psi) \qquad (7) $$

### 2.1.3. Group Delay Derivation

The group delay, $T$, of the wave propagation can be derived from its derivative along the propagation path (Haselgrove, 1957; Yabroff, 1961):

$$ \frac{dT}{ds} = \frac{n^2}{c} \left( 1 + \frac{f}{n} \frac{\partial n}{\partial f} \right) \left( n^2 + \left( \frac{\partial n}{\partial \psi} \right)^2 \right)^{-1/2} \qquad (8) $$

where $s$ is the curvilinear coordinate along the raypath and $c$ is the speed of light in vacuum. The derivative $\partial n/\partial f$ of Equation 7 gives:

$$ \frac{\partial n}{\partial f} = \frac{1}{2f} \sqrt{\frac{S}{M}} \left( \frac{2\mu^2 M}{Y^2 - \mu^2} - \frac{\mu^2}{Y^2 \sqrt{\frac{1}{4} \sin^4 \psi + \frac{\mu^2}{Y^2} \cos^2 \psi}} \right) = \sqrt{\frac{S}{M}} \frac{M_f}{f} \qquad (9) $$

And $\partial n/\partial \psi$.
$$ \frac{\partial n}{\partial \psi} = \frac{1}{2} \sqrt{\frac{S}{M}} \frac{\sin \psi}{\cos^3 \psi} \left( 1 - \frac{\frac{1}{2} \sin^2 \psi + \frac{\mu^2}{Y^2} \cos^2 \psi}{\sqrt{\frac{1}{4} \sin^4 \psi + \frac{\mu^2}{Y^2} \cos^4 \psi}} \right) = \sqrt{\frac{S}{M}} M_{\psi} \quad (10) $$

$M_f$ and $M_ψ$ are introduced for clarity purposes. Both are functions of $f$, $B$ and $ψ$. Using Equations 9 and 10 into Equation 8, we get:

$$ \frac{dT}{ds} = \frac{\sqrt{SM}}{c} \left(1 + \frac{M_f}{M}\right) \left(1 + \frac{M_\psi^2}{M^2}\right)^{-1/2} \quad (11) $$

We now expand $S$ into

$$ S = N \frac{\alpha \mu}{\beta^2 B^2 - \mu^2 f^2} \quad (12) $$

and write the group delay derivative as:

$$ \frac{dT}{ds} = \kappa(f, B, \psi)\sqrt{N} \quad (13) $$

where $\kappa(f, B, \psi)$ is independent of $N$:

$$ \kappa(f, B, \psi) = \frac{1}{c} \sqrt{\frac{\alpha \mu M}{\beta^2 B^2 - \mu^2 f^2}} \left(1 + \frac{M_f}{M}\right) \left(1 + \frac{M_\psi^2}{M^2}\right)^{-1/2} \quad (14) $$

Note that for a given ray with a given frequency $f$, $\kappa$ can be considered as an implicit function of $s$.

### 2.1.4. TREC Definition and Link With $T$

By analogy with the Total Electron Content definition (Budden, 1985, equation 13.52) we define the Total square-Root Electron Content (TREC) as the integration of $\sqrt{N}$ along a given path of total length $s_{sw}$:

$$ \text{TREC}(s_{sw}) = \int_{0}^{s_{sw}} \sqrt{N} \, ds \quad (15) $$

The goal is now to use Equation 13 to derive TREC from the propagation time of whistlers. This is achieved with an integration by parts of Equation 13, for a given frequency $f$ and a given ray. TREC($s_{sw}$) is factored out:

$$ T = \int_{0}^{s_{sw}} \kappa(s) \sqrt{N} \, ds = [\kappa(s_{sw}) - \xi(s_{sw})] \text{TREC}(s_{sw}) \quad (16) $$

where:

$$ \xi(s_{sw}) = \int_{0}^{s_{sw}} \frac{d\kappa}{ds} \frac{\text{TREC}(s)}{\text{TREC}(s_{sw})} ds \quad (17) $$

We computed the values of both $\kappa(s_{sw})$ and $\xi(s_{sw})$ via ray-tracing (see Section 2.2) under experimental whistlers conditions. We obtained the following orders of magnitude: $\kappa(s_{sw}) \sim 10^{-12} \text{ s} \cdot \text{m}^{1/2}$ and $\xi(s_{sw}) \sim 10^{-17} \text{ s} \cdot \text{m}^{1/2}$ (see Figure S2 in Supporting Information S1). $\kappa(s_{sw}) \gg \xi(s_{sw})$ is likely due to the preeminence, in the integral Equation 17, of F region propagation where $\kappa(s)$ is mostly constant. Thus $\xi(s_{sw})$ can be safely neglected and:
$$T = K \text{TREC}(s_{sw}) \qquad (18)$$

where $K = \kappa(s_{sw})$.

## 2.2. TREC Extraction From Whistler Signals

### 2.2.1. Dual-Frequency Method

$T$ cannot be directly inferred from Swarm data, because the time when the whistler enters the ionosphere is unknown. However, the difference of group delay $\Delta T$ between two given frequencies $f_1$ and $f_2$ ($f_1 > f_2$) can be measured. Since propagation is much faster in the Earth-Ionosphere waveguide than in the ionosphere, we can assume that both frequencies entered the ionosphere at the same time. Thus, using Equation 18, one can write:

$$\Delta T = T_2 - T_1 = K_2 \text{TREC}(s_{sw,2}) - K_1 \text{TREC}(s_{sw,1}) \qquad (19)$$

where indices indicate propagation parameters of the two chosen frequencies. Since we assume the ionosphere has spherical symmetry, rays at $f_1$ and $f_2$ propagate through identical ionospheric plasma. For any given ray of a fractional-hop whistler at frequency $f_k$ of path length $s_k$, the function mapping $s_k$ to the radius from the Earth center $r$ is continuous and monotonous between 0 and $s_{sw,k}$. We can thus substitute the variable $s$ with $r$ in the integral. The TREC along the propagation path is then written as an integral between $r_0$, the radius of the base of the ionosphere, and $r_{sw}$, the radius of a Swarm satellite:

$$\text{TREC}(s_{sw,k}) = \int_{0}^{s_{sw,k}} \sqrt{N(s_k)} \, ds_k = \int_{r_0}^{r_{sw}} \sqrt{N(r)} \, \frac{ds_k}{dr} \, dr \qquad (20)$$

We now define two additional parameters, the mean path length $\bar{s}$ and the difference $\sigma$ of the paths with respect to $\bar{s}$:

$$\bar{s} = (s_2 + s_1)/2 \qquad (21)$$

$$\sigma = (s_2 - s_1)/2 \qquad (22)$$

We rewrite the propagation path lengths as $s_1 = \bar{s} - \sigma$ and $s_2 = \bar{s} + \sigma$. Using the linearity of the derivation and integration operations with Equations 19 and 20, we get:

$$\begin{aligned} \Delta T &= K_2 \int_{r_0}^{r_{sw}} \sqrt{N(r)} \, \frac{ds_2}{dr} dr - K_1 \int_{r_0}^{r_{sw}} \sqrt{N(r)} \, \frac{ds_1}{dr} dr \\ &= K_{1,2} \text{TREC}(\bar{s}) + b_{1,2} \end{aligned} \qquad (23)$$

with:

$$K_{1,2} = K_2 - K_1 \qquad (24)$$

$$b_{1,2} = (K_2 + K_1) \int_{r_0}^{r_{sw}} \sqrt{N(r)} \, \frac{d\sigma}{dr} \, dr \qquad (25)$$

where $K_{1,2}$ captures the dependency on the chosen frequencies and $b_{1,2}$ accounts for the separation of the propagation paths for these frequencies. If we can estimate these two parameters, then we can next infer the TREC along the whistler mean path from the measured $\Delta T$.

### 2.2.2. Modeling of the Propagation

Whistler propagation can be modeled via ray-tracing (Yabroff, 1961) using the Hamiltonian formalism proposed by Haselgrove (1957). We implemented the algorithm in MATLAB and chose the adaptive step-size integration method RKF45 (Fehlberg, 1969, p. 13) to solve the equation of the ray. Since the Swarm data do not provide
whistler wave vectors, we cannot compute backward propagation. Instead, the algorithm iteratively searches the suitable entry point of the ray at the base of the ionosphere and performs forward propagation, assuming a vertical initial propagation vector $\vec{k}$ (Helliwell, 1965; Santolík et al., 2009). With this assumption, the condition on $\psi$ guaranteeing Equation 5 becomes a requirement on the local magnetic inclination $I$: $|I| > 1°$. The algorithm computes the monochromatic raypath and group delay $T$. It uses ionospheric profiles, starting at 90 km of altitude, provided by the International Reference Ionosphere (IRI) model IRI-2016 (Bilitza et al., 2017), set up with its default options under the appropriate solar and ionospheric climatological conditions at the location and time of the whistler detection. The magnetic field is approximated locally using a central dipole producing a field matching the 13th International Geomagnetic Reference Field (IGRF) (Alken et al., 2021) model prediction at the time and position of the satellite.

### 2.2.3. A Priori Estimation of $K_{1,2}$ and $b_{1,2}$ Based on Ray-Tracing

For each whistler, ray-tracing through the IRI ionosphere allows us to compute climatological approximations of the raypaths $s_1$ and $s_2$ and group delays $T_1$ and $T_2$ for the two chosen frequencies $f_1$ and $f_2$. From this we infer climatological approximations of $K_{1,2}$ and $b_{1,2}$. The TREC along each path is first calculated by integration of the electron density profile from IRI as described above. The values of $K_1$ and $K_2$ and then $K_{1,2}$ are next derived from $T_1$, $T_2$, TREC($s_1$) and TREC($s_2$). The bias $b_{1,2}$ is deduced from $K_1$ and $K_2$, using Equation 25, where the integral can again be computed from the IRI profile. Under the assumption that these IRI based a priori estimates of $K_{1,2}$ and $b_{1,2}$ are close enough to their real values, Equation 26 can then be used to extract the $TREC_{sw}$ from the $\Delta T_{sw}$ observed by the Swarm satellites:

$$TREC_{sw}(\bar{s}) = \frac{\Delta T_{sw} - b_{1,2}}{K_{1,2}} \qquad (26)$$

The whole process is summarized in Figure 1. As we shall later see, TREC is conveniently quantified by introducing TREC units: 1 TREC = $10^{11} m^{-1/2}$.

## 3. Data Selection for Implementation and Validation of the Method

We selected fractional-hop whistlers detected by Swarm ASM data and validated the TREC method with independent data. Ground ionosondes profiles and in situ electron density measurements have been used to obtain experimental profiles.

### 3.1. Swarm Whistler Data

Whistlers are detected during the 250 Hz burst mode campaigns of the ASMs onboard Swarm Alpha (~450 km) and Bravo (~510 km) acquired 1 week per month per satellite since 2019. The data set now counts more than 100,000 whistlers in the 10–120 Hz band, distributed over a large range of latitudes and Local Times (LT). The events chosen for this initial study, however, are limited to fractional-hop whistlers that were recorded within a 500 km radius from an active ionosonde between May 2020 and July 2022. Information for each event is extracted from the Swarm WHIxEVT_2_product (Coïsson et al., 2023) version 0103, which provides the spectrogram of the magnitude of the magnetic field, as well as parameters inferred from a best fit of this spectrogram to the whistler dispersion equation $D = T\sqrt{f}$ (Eckersley, 1935; Helliwell, 1965, equation 3.21). Using this characterization, the difference in group delay $\Delta T$ between the two reference frequencies $f_1$ and $f_2$ is then obtained (Figure 1b).

### 3.2. Ionosonde Data

To validate the TREC recovered from whistlers against independent data, we rely on three ionosondes of the GIRO network (Reinisch & Galkin, 2011): Ramey (18.50°N, 292.90°E, magnetic inclination $I = 42.37°$), Boa Vista (2.80°N, 299.30°E, $I = 15.46°$) and Santa Maria (–29.73°N, 306.29°E, $I = –39.89°$) (Moro et al., 2020). These were chosen because the number of whistlers occurring within a 500 km horizontal radius are particularly significant. They also provide the opportunity to test our method at three distinct magnetic inclinations, in the northern (Ramey) and southern (Santa Maria) hemispheres, and near the equator (Boa Vista). For each whistlers selected as described above, the closest ionogram in time is selected (7.5 min of delay at most). These ionograms
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Extracting TREC<sub>sw</sub> from whistler data. (a) Logical sequence of the processing steps; (b) Example of whistler spectrogram with group delay ΔT<sub>sw</sub> between the chosen frequencies f<sub>1</sub> = 60 Hz and f<sub>2</sub> = 120 Hz; (c) Example whistler propagation paths independently modeled through ray tracing at frequencies f<sub>1</sub> and f<sub>2</sub> across a climatological ionosphere given by IRI, here close to the Ramey ionosonde location.</figcaption></figure>

have been downloaded from the DIDBase (Digital Ionogram Database Repository at UML in Lowell, USA). To
process these data we use the special SAO Explorer software that can read UMLCAR Digisonde (DPS—Dig-
isonde Portable Sounder) ionogram and scaling data formats (Khmyrov et al., 2008). This allows manual vali-
dation of the automatic evaluation of the sounding data to avoid inaccuracies. It also computes the electron density
profiles. Note that the profiles obtained in this way are constrained by the ionosonde data only up to the peak
electron density $N_m F_2$ of the F2 layer at altitude $h_m F_2$ and that their topside extension above $h_m F_2$ are only extrapolations based on the technique of Reinisch and Huang (2001).

### 3.3. Swarm In Situ Electron Density Measurements

To construct alternative experimentally constrained topside profiles, we also take advantage of in situ 2 Hz electron density measurements independently provided by the Swarm Langmuir Probes (LP) (Knudsen et al., 2017) and rely on the NeQuick 2 topside function (Nava et al., 2008). More specifically, we use the ionosonde $N_m F_2$ and $h_m F_2$ values and next adjust the topside thickness parameter to match the LP data. These LP data are obtained from the ESA EFIx_LP_1B_data set version 0602 and selected for the time matching the whistler detection time. The value used to construct the topside profile is the median of the 20 closest points.

In the remainder of this paper, the above data are analysed as three separate data sets, one for each ionosonde location. Figure S3 in Supporting Information S1 illustrates some of their key characteristics and how they match the above selection criteria. Note, however, that two additional smaller data sets for two mid-latitude ionosondes (Millstone Hill, 42.60°N, 288.50°E, magnetic inclination $I = 66.7°$ and Grahamstown, -33.30°N, 26.50°E, $I = -63.0°$) were also later assembled, analyzed and discussed for further validation (see Supporting Information S1).

## 4. Validation of the TREC Extraction Method

We implement the TREC extraction method to Swarm whistler data. Since $f_{gi} \le 38$ Hz above the studied areas, we choose $f_1 = 120$ Hz and $f_2 = 60$ Hz. $f_2$ is chosen to comply with the hypotheses of Section 2. $f_1$ is chosen at the top the ASM bandwidth to ensure maximum frequency separation.

Our validation strategy is to compare TREC recovered from Swarm whistlers (Swarm TREC, hereafter) to TREC predicted by integration of profiles provided by the IRI model, the ionosondes and in situ electron density measurements. The TREC predicted from the IRI model (IRI TREC) provides the a priori value of the TREC. This IRI TREC is the default TREC value one can estimate in absence of any local sounding of the ionosphere. In contrast, the TREC predicted from the ionosonde local profile (Iono TREC), and that predicted from the profile further constrained by the in situ electron density measurements (Iono + LP TREC), can be expected to be more representative of the sampled TREC at the time of the whistler propagation.

To first understand the consequence of using LP data to constrain the predicted TREC, we plotted the distribution of the difference between Iono + LP and Iono TREC predictions (Figures 2a–2c). For the vast majority of events, the predicted Iono + LP TREC differs from the predicted Iono TREC by typically some 0.1 TRECu, with a tendency to predict higher values (especially for Ramey and Santa-Maria). In the Ramey data set (Figure 2a), however, a group of 10 events clearly stands out, with TREC differences reaching nearly 1 TRECu. They correspond to consecutive whistlers detected within 1 min along a single orbit of Swarm Bravo around 19.1 LT on 24 August 2020. This LT is shortly after the solar terminator passed over the region, when unstable ionospheric conditions may occur (Afraimovich, 2008; Afraimovich et al., 2009). Since the ionosonde soundings and the LP measurements are not exactly co-located and synchronous, this may well have led to an inappropriate reconstruction of the topside ionospheric profile used to compute the Iono + LP TREC. In what follows, to avoid including any doubtful topside profiles when testing the TREC extraction method, we remove these 10 events from our final validation data set. For Boa Vista, (Figure 2b), only two predicted Iono + LP TREC are beyond $4\sigma$ within the distribution, with no identified explanation for this behavior. For consistency, we also exclude these two events in the validation data set. No outliers have been otherwise identified at Santa Maria (Figure 2c), and all events were kept for that location.

Figures 2d–2f show the outcome of comparing IRI, Iono, and Iono + LP predicted TRECs to the Swarm TREC when using the final test data set. As can be seen, IRI TREC values (blue) are already well correlated with the Swarm TREC estimates. This is true at all three ionosonde locations. However, IRI TREC values are clearly systematically offset upward and substantially scattered about the corresponding best linear fit (blue line). Encouragingly, the situation is much improved when considering Iono TREC values (green). Both the offset and scattering are now reduced. Comparing the Swarm TREC with the Iono + LP TREC (red) shows even further improvement, though in a more subtle way in the case of Boa Vista. This is expected, since Boa Vista is where Iono + LP and Iono TRECs least differ (Figure 2b).
<figure><img src="image_3.png" /><figcaption>**Figure 2.** TREC validation results; First column: Distribution of the difference between predicted Iono + LP and Iono TRECs at each ionosonde station (Ramey (a), Boa Vista (b) and Santa Maria (c)). Only events from the main distribution (black) are kept for the validation study (rejected outliers identified in hatched). Second column: Correlation between Swarm TREC (horizontal axis) and predicted TREC values (vertical axis) for whistlers of the three ionosonde locations (Ramey (d), 91 whistlers, Boa Vista (e), 143 whistlers and Santa Maria (f), 151 whistlers). IRI TREC, Iono TREC and Iono + LP TREC are respectively shown in blue, green and red. Both vertical and horizontal axis are in TREC units. All TRECs are computed along the average IRI ray-tracing path. The dashed gray line is the bisector of the graph (perfect correlation).</figcaption></figure>
<table><caption>**Table 1**
Results of the Linear Regressions Between Predicted and Swarm TRECs</caption><thead><tr><th>Location</th><th>Source</th><th>N</th><th>Slope</th><th>Intercept</th><th>RMSE</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td rowspan="3">Ramey</td><td>IRI</td><td>91</td><td>1.07(7)</td><td>0.4(1)</td><td>0.126</td><td>0.727</td></tr><tr><td>Iono</td><td>91</td><td>1.12(5)</td><td>-0.07(7)</td><td>0.060</td><td>0.861</td></tr><tr><td>Iono + LP</td><td>91</td><td>1.02(4)</td><td>0.15(6)</td><td>0.041</td><td>0.883</td></tr><tr><td rowspan="3">Boa Vista</td><td>IRI</td><td>143</td><td>0.90(5)</td><td>0.40(9)</td><td>0.130</td><td>0.732</td></tr><tr><td>Iono</td><td>143</td><td>0.99(4)</td><td>0.16(7)</td><td>0.078</td><td>0.846</td></tr><tr><td>Iono + LP</td><td>143</td><td>0.96(3)</td><td>0.21(7)</td><td>0.067</td><td>0.859</td></tr><tr><td rowspan="3">Santa Maria</td><td>IRI</td><td>151</td><td>0.94(3)</td><td>0.34(5)</td><td>0.051</td><td>0.890</td></tr><tr><td>Iono</td><td>151</td><td>0.96(3)</td><td>-0.10(5)</td><td>0.052</td><td>0.892</td></tr><tr><td>Iono + LP</td><td>151</td><td>0.94(2)</td><td>0.11(3)</td><td>0.023</td><td>0.948</td></tr></tbody></table>

Note. N is the number of selected whistlers. The linear regression standard errors are indicated for the slope and the intercept in parenthesis. RMSE and intercept are both in TREC units.

Table 1 provides various indicators associated with the linear fits (solid lines) plotted in Figures 2d–2f. These can now be used to quantify the previous initial assessment. We first focus on the R² and RMSE parameters. R² provides a measure of adequacy of the assumption that IRI, Iono and Iono + LP predicted TRECs can be linearly related to the Swarm TREC, while RMSE provides a measure of the scattering of data points with respect to the best linear fits, both independently of what the recovered slope and intercept values of the best linear fits may be. Perfect correlation implies R² = 1 and RMSE = 0. These parameters confirm that a better fit is achieved to the Swarm TREC, with less scattering, at all three locations when moving from the IRI TREC to the better informed iono TREC and next to the even better informed Iono + LP TREC. These results are those one would expect if (a) the Swarm TREC provides a proper measure of the TREC, which is what we wanted to test, and (b) the Iono TREC, and even more so the Iono + LP TREC, are more representative of the real TREC than the IRI TREC. Particularly worth noting is that the comparison of the Swarm TREC with the Iono + LP TREC does bring further improvement, despite differences between Iono + LP and Iono TREC predictions within ranges of several 0.1 TRECu, much higher than the RMSE values. Such an improvement cannot be the result of sheer chance.

## 5. Discussion

Beyond showing that progressively more informed TREC predictions better correlate with the recovered Swarm TREC, Table 1 also provides useful information about systematic trends when comparing predicted IRI, Iono, and Iono + LP TRECs with Swarm TREC. Figures 2d–2f and slope and intercept values in Table 1 all point at the IRI TREC values overestimating Swarm TREC by a systematic offset of about 0.4 TRECu for Ramey, by similar amounts for Boa Vista and Santa Maria when the TREC is small, but less so for high values. Clearly, the IRI model tends to always overestimate that part of the electron density profile to which the Swarm TREC is sensitive. In contrast, Iono TREC values are much less offset when compared to Swarm TREC, though predictions at Ramey still tend to overestimate large TREC values, while predictions at Santa Maria now tend to systematically slightly underestimate Swarm TREC. This is a positive indication that profiles constructed from ionosondes with only default information to reconstruct the topside profile presumably capture appropriate information about the bottom-side profile but are still missing reliable topside information to properly predict the Swarm TREC.

Finally, the Iono + LP profiles, which we saw tend to predict larger TREC values than the Iono profiles at both Ramey and Santa Maria (Figures 2a and 2c), predict TRECs much more in line with the Swarm TREC. At Ramey, Swarm TREC is slightly over-predicted for all TREC values (by 0.15 TRECu), while at Boa Vista and Santa Maria this is only the case for small TREC values, with a slight trend to under-predict large TREC values at Santa Maria. Clearly the additional local information provided by the Swarm Langmuir Probe and the use of the NeQuick 2 topside functions bring further improvement to the electron density profile to which the Swarm TREC is sensitive. As discussed in Supporting Information S1, these conclusions also hold at mid-latitudes when analyzing the two smaller Millstone Hill and Grahamstown data sets (Figure S5 and Table S1 in Supporting Information S1).

There are many reasons why Iono + LP TREC may still not properly predict the observed Swarm TREC. One lies in the necessarily limited accuracy of the methodology we introduced to reconstruct TREC from Swarm whistlers. This method relies on a number of assumptions and approximations, the limits of which remain to be assessed. Whistler data are themselves also affected by uncertainties, which we ignored. The Iono + LP TREC used for comparison with Swarm TREC rely on ionosonde profiles affected by uncertainties, equally ignored. The NeQuick 2 topside function used to constrain the top-side electron profile with just a single electron density value provided by the Swarm LP data is also a potential source of uncertainty. Indeed, Swarm LP in situ data may require corrections (Lomidze et al., 2018; Smirnov et al., 2021). Last but not least, Swarm TRECs are never sensing the ionosphere at the exact same time and geographic location as the profiles used for Iono + LP TREC predictions. Considering all these limitations, it is quite remarkable that TREC recovered from Swarm whistlers using the methodology we introduced already much better reproduces Iono + LP TREC predicted from profiles constrained by ionosondes and Swarm local LP data, than the default climatological IRI TREC prediction.
## 6. Conclusions

Relying on propagation theory of ELF waves in the ionosphere, we highlighted a link between ELF whistlers and a new metric of the state of ionization of the ionosphere, the TREC. We developed a method to derive TREC estimates from the many whistlers that can be detected by space-born magnetometers, tested it using whistlers detected by the ASM magnetometers onboard the Swarm satellites and successfully validated it against predictions based on the IRI climatological model as well as on improved models constrained by ionograms from three ionosondes and Swarm in situ LP electron density data. Our results show that this method can be used to provide new constraints on the state of the ionosphere below LEO. Since the method does not require any ground equipment, it opens remote sensing capabilities of the ionosphere above remote or oceanic sectors. This technique can be adapted to other satellite carrying magnetometers with ELF whistlers detection capabilities within the relevant 30 Hz to a couple of kHz frequency range (as suggested by Figure S1 in Supporting Information S1). Data from other missions with such capabilities, such as DEMETER (Detection of ElectroMagnetic Emissions Transmitted from Earthquake Regions) (Parrot et al., 2006) or the future NanoMagSat ESA Scout mission (Hulot et al., 2018, 2021), could therefore also be exploited to measure TRECs and provide new study angles of the ionosphere to the community.

## Data Availability Statement

The ionosonde data used in this study can be viewed publicly and accessed from the GIRO database http://spase.info/SMWG/Observatory/GIRO. The Swarm mission data can be publicly accessed from the ESA server https://swarm-diss.eo.esa.int. The IRI model is available from http://irimodel.org.

## Acknowledgments

The ASM instrument was developed by CEA-Léti and provided as Customer Furnished Instrument by CNES. The authors acknowledge the ESA Swarm team for the support provided in acquiring ASM burst-mode data and for the successful operations of the mission. The development of the WHIxEVENT_2_production chain was started during project "Investigating Lightning Generated ELF Whistlers to improve ionospheric models" (ILGEW), ESA contract No. 4000126708/19/NL/IA and implemented under ESA Swarm DISC contract No. 4000109587 (DTU sub-contract SW-CO-DTU-GS-010). This project was financially supported by the Centre National d'Etudes Spatiales (CNES) as an application of the Swarm mission, through project "Suivi et exploitation de la mission Swarm." The PhD thesis of M.J. is partly supported by CNES. The authors acknowledge the institutes providing and supporting GIRO activities. Data from the Brazilian Ionosonde network is made available through the EMBRACE program from the National Institute for Space Research (INPE). Data from the South African Ionosonde network is made available through the South African National Space Agency (SANSA), who are acknowledged for facilitating and coordinating the continued availability of data. The authors finally wish to thank two anonymous reviewers for their insightful and very useful comments.

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