# Ionospheric electron density profiles inverted from a spectral riometer measurement

A. Kero,

## Abstract

The first implementation of the so-called *spectral riometer* technique for the ionospheric electron density profile estimation is presented. In contrast to the traditional riometer operating at a single frequency, this experiment monitors the cosmic radio noise at 244 frequencies, ranging between 10 and 80 MHz, by using the new Kilpisj rvi Atmospheric Imaging Receiver Array radio telescope. The received power at each time and frequency is compared to the corresponding quiet-day value, resulting in the cosmic radio noise absorption spectrum as a measurement of ionization in the ionosphere. In this study, the observed absorption spectrum is used to invert the corresponding electron density profile by applying a simple parameterized electron precipitation model. By comparing the inverted electron density profiles to a simultaneous and nearly colocated European Incoherent Scatter VHF radar measurement on 13–14 November 2012, we show that the spectral riometry approach is capable of producing realistic electron density profiles under conditions of substorm-related electron precipitation.

## Key Points

- Spectral riometer measurement is introduced and implemented for the first time
- A novel inversion of the ionospheric electron density profile is presented
- A good general agreement with the EISCAT reference data is found

## 1 Introduction

Electron density response to variable ionization at the mesosphere-lower thermosphere altitudes provides useful information on both the ionization source processes (solar electromagnetic radiation, particle precipitation, and cosmic rays) and their consequences on the atmosphere (e.g., chemical changes due to ionization). While global monitoring of the ionization sources is generally well covered by spaceborne instruments, the satellites struggle to measure accurately the precipitating particle fluxes [e.g., *Rodger et al.*, 2010]. Therefore, continuous measurements of electron density profiles would potentially be of key importance in studying the effects of the solar activity via the particle precipitation in the upper atmosphere.

One of the most cost-effective remote sensing method for lower ionospheric ionization is the riometer (relative ionospheric opacity meter). When the cosmic radio noise propagates through a collisional plasma of the ionosphere, a part of its energy is transferred into the thermal energy of the plasma in collisions between electrons and neutrals. The amount of radio wave absorption, in decibels, is approximately proportional to , where *N*_{e}, *ν*_{en}, *ω*, and *ω*_{L} are electron density, electron-to-neutral collision frequency, radio wave angular frequency, and angular gyrofrequency of electrons, respectively. As a product of electron density and the “absorption sensitivity” governed by the characteristic frequencies *ν*_{en}, *ω*, and *ω*_{L}, the absorption maximizes at the *D* region ionosphere in which both *N*_{e} and *ν*_{en} are sufficiently high.

This technique was first used by *Shain* [1951]. For a complete review of the early riometry results, see *Hargreaves* [1969]. A major technical advance in riometry was introduced in the 1990s by the imaging riometers capable of receiving the cosmic radio noise from a set of beams across the sky [*Detrick and Rosenberg*, 1990]. Latest advances in imaging riometry are reviewed in *Honary et al.* [2011].

The approach of using riometer measurements at multiple frequencies to determine the electron density profile was first proposed already in *Parthasarathy et al.* [1963], followed by several authors suggesting alternative methods [*Belikovich et al.*, 1964; *Lerfald et al.*, 1964; *Hultqvist*, 1968; *Musser*, 1969; *Jusick and Furman*, 1969; *Lavergnat and Berthelier*, 1973]. Despite high scientific importance of electron density inversion, multifrequency riometry has not been utilized in the routine ionospheric research up-to-date. Instead, both the wide-beam and the imaging riometers have been operated at some single frequency for continuous monitoring of the ionospheric ionization. This might have been due to technical limitations, i.e., the aforementioned studies considered only a few (typically 2–3) different frequencies and, related to that, the electron density inversion turns out to be too unstable for reliable profile estimation. With the present technology, however, it is possible to cover the whole cosmic radio noise absorption spectrum with tens or hundreds of individual frequency bands. Moreover, modern nonlinear Bayesian inversion methods make it possible to fully exploit the information content of the measurement.

## 2 KAIRA Spectral Riometer Measurement

The experiment was carried out using the Kilpisjärvi Atmospheric Imaging Receiver Array (KAIRA; 69.1°N, 20.8°E, magnetic *L* value = 6.2) station, which comprises two arrays of omnidirectional Low-Frequency Array (LOFAR) VHF radio antennas. The Low-Band Antenna array used for the riometry has 48 cross-dipole antennas scattered quasi-randomly across a field approximately 34 m in diameter, providing 10–20° beam widths (at zenith) in the frequency range used. The LOFAR digital signal-processing hardware [*van Haarlem et al.*, 2013] can form 244 so-called “beamlets,” i.e., receiver beams with a narrow-frequency band (BW = 195.3 kHz) around a freely selected center frequency and an arbitrary pointing direction. In the experiment presented, all the beamlets were zenith pointed, enabling the recording of the cosmic radio noise at 244 different frequencies simultaneously in a 1 s resolution.

*P*

_{q}and

*P*are the quiet-day and the observed power, respectively. For this proof-of-concept study, we selected the frequency range 17–55 MHz (horizontal dashed lines in Figure 1), where the cosmic radio noise is expected to clearly dominate over the receiver noise, and the band is mostly free from radio transmitter interference. Events of suddenly increasing absorption in Figure 1c, corresponding to attenuations in Figure 1a, show clear signatures of significant excess ionization in the ionospheric

*D*region. This is confirmed by simultaneous (21–05 UT) and nearly collocated (69.9°N, 19.2°E, and 85 km in distance) European Incoherent Scatter (EISCAT) VHF incoherent scatter measurement in Figure 2b, showing that the excess ionization is due to the energetic electron precipitation, likely associated with the concurrent auroral substorm activity. The simultaneous EISCAT reference data enable an independent quantitative validation for electron density profile estimation by the spectral riometry presented here.

## 3 Inversion of the Electron Density Profile

### 3.1 Model for the Absorption Spectrum

To model the radio wave absorption as a function of frequency, the generalized Appleton theory given by *Sen and Wyller* [1960] was applied to obtain the complex refractive index *n* = *R**n* + *i**I**n* for both circular polarizations, *n*_{o} and *n*_{x}, at each height *h* and frequency *f* of interest. The refractive index depends on the radio wave frequency, electron density *N*_{e}, electron-to-neutral collision frequency, and, to a lesser degree, the external magnetic field. The collision frequency is calculated here as in *Dalgarno et al.* [1967], based on the NRL-MSISE-00 reference atmosphere [*Picone et al.*, 2002], and a simple dipole approximation was used for the Earth's magnetic field. The quiet background electron density profile *N*_{eq}(*h*), needed to calculate the corresponding refractive indices *n*_{oq}(*h*,*f*)and *n*_{xq}(*h*,*f*), was obtained by using the Sodankylä coupled Ion-neutral Chemistry (SIC) model [*Turunen et al.*, 2009]. Similarly, the refractive indices *n*_{o}(*h*,*f*), *n*_{x}(*h*,*f*) can be calculated for the instantaneous electron density profile *N*_{e}(*h*).

*c*is the speed of light and the subscript “

*s*” is replaced by “

*o*,” “

*x*,” “

*oq*,” or “

*xq*.” The theoretical absorption spectrum (equation 2) can now be evaluated for any proposal of an electron density profile

*N*

_{e}(

*h*) and compared against the measurement (equation 1) in the least squares sense. Hence, the next task is to find a feasible method for generating realistic electron density profile proposals, with as few parameters as possible, to be used in the inversion.

### 3.2 Parameterized Electron Density Profile

The pioneering multifrequency riometry studies pointed out that the electron density profile inversion is a highly ill posed problem, hence needing some strong regularization in order to obtain stable results. Therefore, rather than trying to solve the electron density at different heights independently, a parameterized model providing smooth *N*_{e}(*h*) profiles has to be used.

*Parthasarathy et al.* [1963] used a polynomial expansion to model the electron density profile to obtain a linear relation between the measurements and the unknowns. Another approach was taken by *Belikovich et al.* [1964] and later *Hultqvist* [1968], who used substitution of variables to convert the logarithmic absorption into a convolution equation, which also provides a proof of a unique solution if all the derivatives of absorption can be measured at all frequencies. Out of the early studies of multifrequency riometry, the approach adopted here most closely resembles that of *Musser* [1969], in which the electron density profile was obtained by a simple model based on the ionization by solar protons. In our study, the excess electron density causing the increased absorption is interpreted in terms of electron precipitation.

*Q*

_{0}, ionization by the electron precipitation

*Q*and recombination rate

*L*. In the absence of negative ions, the electron density budget is governed by

*N*

_{e}/d

*t*= 0), and a timewise constant recombination rate

*L*, we get

*N*

_{eq}are both calculated with the SIC model. The electron precipitation part of the ionization is calculated according to

*Rees*[1989, pp. 35–45]:

*Λ*is the energy dissipation function for monoenergetic electrons of isotropic angular dispersion up to 80° [

*Rees*, 1963],

*ρ*(

*h*) is the mass density based on the reference atmosphere [

*Picone et al.*, 2002],

*R*(

*E*) is the effective range of the electrons, and

*Δ*

*ϵ*

_{ion}=35 eV is the energy loss per ion pair formation. The energy spectrum is assumed to be exponential, i.e.,

*γ*= 0 and characterized by the energy

*E*

_{c}and flux

*J*

_{0}. Thus, the forward model of the electron density profile (equation 5), and hence the desired absorption spectrum (equation 2), can be evaluated as a function of the two free parameters

*E*

_{c}and

*J*

_{0}.

### 3.3 Electron Density Profile Inversion

To find the posteriori probability distribution of these two free parameters *E*_{c} and *J*_{0}, based on the least squares fit between the measured absorption spectrum (equation 1) and the parameterized model (equation 2), the Delayed Rejection Adaptive Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm [*Haario et al.*, 2006] was used. For computational stability, the base-10 logarithms of the parameters were searched in the ranges log10(*E*_{c} [keV])∈[0,2] and log10(*J*_{0} [m^{−2}s^{−1}sr^{−1}keV^{−1}])∈[3,15]. The MCMC chain length was set to 10,000, providing converging solutions in the vast majority of the cases. The MCMC inversion was applied to 1 min average absorption spectra in the interval 19–05 UT. The results are shown in Figure 2 and discussed in the following.

## 4 Discussion

As seen in Figure 2 the electron density profiles inverted from spectral riometer data are found to be in a good general agreement with simultaneous EISCAT VHF radar measurements. The standard analysis routines used to retrieve electron densities from EISCAT data are not optimal for the *D* region, but it can be seen that the magnitude and the cutoff altitude of the excess ionization are reproduced. In a close comparison, the riometry underestimates the strongest peaks of the ionization and overestimates the electron density during the quiet moments. These discrepancies are consistent with absorptions calculated for the EISCAT VHF electron density profiles (not shown), i.e., the EISCAT VHF detects remarkably more variable ionization compared to the KAIRA data. The discrepancy is likely due to the different measurement volumes, not only the locations but also the beam widths. High-resolution auroral imager data [e.g., *Dahlgren et al.*, [2008] reveal that energetic precipitation appears as rapidly moving thin filaments which are likely beam filling for the narrow EISCAT VHF beam, whereas the wider KAIRA beam averages out the fine structures and results less temporal variation.

The forward model of the absorption spectrum used in the inversion (equation 2) is determined by the height integral of the differential absorptions (equation 3). In the cases studied, the peak radio noise absorption was at altitudes between 80 and 100 km, and hence, to reproduce the observed absorption spectrum, the MCMC inversion tends to scale the electron density profile to the best fit in this most significant altitude range. However, since the modeled electron density profile is determined solely by the two parameters *E*_{c} and *J*_{0}, it extends also below and above these altitudes. One should be cautious in generalizing the riometry results far outside the actual altitudes of absorption, but at least in this case, the EISCAT VHF reference data support the electron densities predicted by the precipitation model up into the *E* region.

The inversion was based on finding the two characteristic parameters (*E*_{c} and *J*_{0}) determining the excess ionization (equation 6) under the assumptions of a chemical equilibrium, a static recombination rate and absence of negative ions in the target plasma. It is questionable how well these assumptions hold in reality, especially in the case of strong electron precipitation. Thus, one should be cautious of potential biases in the energies and fluxes (Figure 2c). Moreover, it is worth to note the correlation between the two parameters, pointing at the fact that different precipitation parameter pairs can produce approximately equal electron density profiles at the altitudes of the maximum absorption. Comparison to the EISCAT data demonstrates, however, that the MCMC inversion of the two-parameter model was successful in resolving altitude profiles of electron density during the studied event.

## 5 Conclusions

We have shown that spectral riometer measurement, combined with a model of electron precipitation, is capable of producing realistic electron density height profiles compared to simultaneous and nearly collocated incoherent scatter radar measurements. This proof-of-concept study builds confidence toward continuous measurements of electron density height profiles during events of excess ionization, such as auroral substorms.

## Acknowledgments

This work has been partly funded by the Academy of Finland: project 250215, Finnish Programme for Centres of Excellence 2012–2017 and Postdoctoral research project 134439, 2010–2012. We are indebted to the director and staff of EISCAT for operating the facility and supplying the data. EISCAT is an international association supported by research organizations in China (CRIRP), Finland (SA), Japan (NIPR and STEL), Norway (NFR), Sweden (VR), and the United Kingdom (NERC). Following the data policy of AGU, all the data presented here are curated and made available upon request by the Sodankylä Geophysical Observatory (www.sgo.fi).

The Editor thanks Martin Friedrich and an anonymous reviewer for their assistance in evaluating this paper.