Cosmic noise at 40 MHz is measured at Ny-Ålesund (79

The relative ionospheric opacity meter (“riometer”) is a traditional instrument for measuring the degree to which cosmic noise is absorbed by the ionosphere (e.g. Little and Leinbach, 1959). By selecting a particular frequency for the riometer reception, it is possible to optimise the sensitivity to a particular altitude range and therefore how energetic the particles are that are causing the ionisation. The means of analysing the signal from the riometer is to determine the “quiet-day” variation and thereafter the degree of absorption caused by the intervening ionosphere. For a given radio wave frequency, the transmission, total reflection, partial reflection or absorption is indicated by the refractive index of the atmosphere. The refractive index of an ionised medium is in turn related to plasma parameters and the frequency of the radio wave in question by the Appleton–Hartree equation; this is thus a starting point for understanding the response of the riometer signal to varying degrees of particle precipitation (Hargreaves, 1979, 1992). Here however, the signal in its original form, as opposed to the derived absorption, will be examined, i.e. the cosmic noise as measured by a receiver at the Earth's surface, since the object of this study is to investigate the spectrum of the signal itself including intermittency introduced by solar activity. Investigating the signal in this way will, of course, convolve several physical effects, including those due to the sun, in the ionosphere and in the instrument itself. The physical interpretation of the results will be somewhat obscured, but the intention here is to use this technique as a supplementary tool combined with other instrumentation, or to help validate new instrumental development.

Data have been obtained from the recently established 40 MHz single-beam
riometer at Ny-Ålesund (79

As mentioned above, the idea of the riometer is to determine the absorption
of cosmic noise due to perturbations in the intervening ionosphere due to
space weather effects. These perturbations, in contrast to the largely
deterministic quasi-diurnal and longer periods, end up being intra-diurnal and
often of only

Cosmic noise at 40 MHz measured by riometer at Ny-Ålesund,
79

A significant problem in the study of physical systems is the identification
of coupling between processes that are causes and that are true effects. An
evolving approach is to examine the stochastic nature of the signals from
different processes because noise present in a cause will presumably also be
present in resulting effects. The noise signatures may not be unambiguous of
course, so any apparent coupling must be treated with care. Although gaining
popularity, the principle was introduced by, inter alios, Hurst (1951),
Mandelbrot (1983), Grassberger and Procaccia (1983) and Koscielny-Bunde et
al. (1998) and later explored by e.g. Eichner et al. (2003), Lennartz and
Bunde (2009), Kantelhardt et al. (2006), Rypdal and Rypdal (2011) and Hall (2014a, b).
The concepts of fractional Gaussian noise (fGn) and
fractional Brownian motion (fBm) were proposed by Mandelbrot and van
Ness (1968), and the Hurst exponent,

Detail plot of cosmic noise at 40 MHz measured by riometer at
Ny-Ålesund, 79

Using the approach of Hall (2014a, b), the stochastic component of the time series is isolated from the slowly evolving (deterministic) component. Here, a smoothed time series will be subtracted from the original, and the residual will be deemed stochastic, as will be demonstrated in the following section. From the stochastic (noise) component, the probability density function (PDF) of the data is obtained, and thereafter quantile–quantile (Q–Q) analyses (Wilk and Gnanadesikan, 1968) performed. To produce Q–Q plots, quantiles of the distribution of signal noise are plotted against corresponding quantiles for hypothesised distributions exhibiting the same mean and standard deviation. A visual inspection of the PDF can indicate if the signal's noise distribution is Gaussian or otherwise. From an inspection of the Q–Q plots the degree to which the signal's noise distribution agrees with that hypothesised: a straight line indicating agreement.

In this study, the goal is to investigate the spectrum of the cosmic noise data in their entirety, encompassing variations at all timescales, and see if well-defined subranges exist that can be related to known physics. The starting point is not, therefore, a derived stochastic component. Furthermore, experimental data, including gaps due to instrument failure, are almost invariably irregularly sampled, and therefore the Lomb–Scargle periodogram analysis (Press and Rybicki, 1989) will be used rather than a traditional Fourier transform. Fougère (1985) and Eke et al. (2000) propose preconditioning of the time series by applying a parabolic window, thereafter bridge detrending using the first and last points in the series, and then a final frequency selection before identifying subranges exhibiting linear dependence in log–log space. This last step however will be omitted in order to retain as much spectral information as possible, at least initially.

Portrayals of the distribution of the stochastic component (described in the text) of the cosmic noise signal. Left: probability density function with fitted Gaussian (red) and Cauchy (blue) distributions superimposed (explained and discussed in the text). Centre: Q–Q plot of the observed data versus Gaussian; right: Q–Q plot of the observed data versus Cauchy.

It should be mentioned that several approaches are available for estimating

As described in the previous section, an approximation to the stochastic
component of the cosmic noise signal is extracted from the complete dataset.
Which timescales contain deterministic signals is open to discussion; since
perturbations resulting from solar–terrestrial interaction can recur over
periods of days (such as some polar cap absorption events), the time series
shown in Fig. 1. has been deemed deterministic. This is then subtracted from
the original, and the residual deemed largely stochastic. A corresponding
method was employed by Hall (2014b). As will be seen, spectral analysis
identifies individual periodicities remaining in the (supposedly) stochastic
residual, these showing up as narrow spikes. Due to the large number of data
points and therefore frequencies in the spectrum, these spikes impose
insignificant influence when determining the spectral slope. A disadvantage
with DFA is that such periodicities are generally

A number of studies have hypothesised that solar fluctuations give rise to
processes that may be characterised by Lévy walks or flights, e.g.
Scafetta and West (2003) and Watkins et al. (2005) (and references therein).
As explained by Sato (1999), a Cauchy process is defined as Brownian motion
subordinated to a process associated with a Lévy distribution. The
earlier analyses of solar and ionospheric observables are therefore
considered a justification for comparing a Cauchy distribution as well as
Gaussian with that of the riometer data. The probability density function (distribution)
of the stochastic component of the data is determined and
shown in Fig. 3. The distribution is centred on zero, resulting from
subtraction of the deterministic component. A Gaussian distribution is
fitted that fails to reproduce the narrowness of the distribution of the
observation at half height. By using a different parameterisation of the
distribution width than full width at half maximum, viz. 1

For determination of power spectral density, the entire original dataset is
employed, such that all conceivable fluctuations are included. There are
therefore no a priori assumptions as to which fluctuations are truly
non-chaotic. The exception is the sidereal periodicity, but as stated
earlier, this represents but one narrow spike in the spectrum compared with
all other frequencies present and does not influence the identification of
subranges exhibiting scaling and subsequent determination of exponents

Spectral analysis for data shown in previous figures. Familiar timescales are indicated by vertical dotted/dashed lines. Fitted scaling exponents are shown by coloured lines. The horizontal dashed line indicates the 95 % confidence level.

The first characteristic to note is that, for all variability in 40 MHz cosmic
noise at timescales shorter than 1 month, the probability density function
is not well represented by a Gaussian distribution. The attempt to fit a
Cauchy distribution defining the width being at

Turning to the spectral analysis, there is an indication that three subranges
are present in the spectrum. Timescales associated with auroral activity
which, in turn, correspond to enhanced electron densities in the ionospheric
D-region are typically minutes to hours. One can envisage an auroral arc
moving across the sky; although this will be in one position for a short
time interval, it will be in the riometer antenna beam for much longer. The
response of a ground-based magnetometer is similar to that described by Hall
(2014b), although current systems causing perturbations in the geomagnetic
field typically occur at higher altitude than ionisation modulating cosmic
noise at 40 MHz. It can therefore be hypothesised that the scaling exponent
for periods > 1 h is associated with absorption events and,
at that, caused by high-energy precipitation, since the riometer is within
the auroral oval and receives at 40 MHz. Furthermore variation in cosmic
noise itself over timescales of hours is slow, and particularly so for an
instrument averaging signal of a large part of the sky at high latitude (a
narrow-beam riometer would respond to more discrete signals and detect
shorter-term variability). If the reader is unfamiliar with ionospheric
physics, clarification can be obtained by reading appropriate chapters in e.g.
Hargreaves (1979, 1992), and the recent study by Kellerman et al. (2014)
contains an exhaustive source of references. For periods > 1 day,
variation of the signal is largely predicable from the geometry of
the rotation of the observation point relative to the galaxy. Nevertheless,
solar activity responsible for polar cap absorption events can persist for
consecutive days, and the associated absorption is modulated by the Earth's
rotation and compounded by ion chemistry. For the shortest timescales before
the onset of the approximately white instrumental noise described earlier,
it is somewhat unclear as to which processes are responsible for the less
steep (

In summary, three spectral subranges can be identified apart from the white
noise deemed instrumental: a short-timescale regime of the order of minutes
to hours, exhibiting 1

Cosmic noise signal at 40 MHz has been recorded at 79

Solar variability and its interaction with the terrestrial ionosphere is
popularly known as space weather. The ionospheric response has typical
timescales of hours but may repeat over consecutive days due to the Earth's
rotation and over weeks due to the Sun's rotation. Signal variation with
scales of

Underlying physical processes can be identified in riometer data by classification in terms of the generalised Hurst exponent. The study here therefore contributes to the growing arsenal of statistical classifications of signals from different instruments and their links to physical processes originating outside the solar system, in solar–terrestrial relations and even in the neutral atmosphere, including possible anthropogenic forcing.

It must be stressed that this study in no way attempts to present a means of measuring physical parameters by spectral classification alone; indeed, known physics are used here to provide plausibility to the existence of the spectral subranges and thus corresponding Hurst exponents. The method is presented as a supplementary tool for example for helping remove ambiguities from results from other observations. New instrumentation (including, for example, innovative riometers) could also be validated by comparing spectral characteristics.

Subsequent investigation could include examination of cosmic noise signals at both 30 and 40 MHz, with their respective responses to precipitating particle energies, from receivers within, under and outside the aurora oval, together with corresponding magnetometer analyses. Such results would be valuable not only to substantiate the aforementioned hypotheses but more importantly to establish dependence of the spectral characteristic on geomagnetic latitude and energies of precipitating particles.

Finally, it must be stressed that the analysis techniques employed in this study unfortunately failed to result in clear physical understanding of ionospheric phenomena and thus, in this respect, the application was not successful. In fact, the reverse is more the case: cosmic, solar, ionospheric and instrumental effects may be identified in the results such that the technique is better suited as a tool for instrument development and validation.

The data used by this study are from a pilot experiment and as such are
freely available but not otherwise published in any publicly accessible
database. The data can nonetheless be provided by Tromsø Geophysical
Observatory on request via contact information to be found on the Observatory
website

Data from the Ny-Ålesund station can be obtained via Tromsø Geophysical Observatory. Edited by: B. Tsurutani Reviewed by: two anonymous referees