Environmental sources of radio frequency noise: potential impacts on magnetoreception

Abstract

Radio frequency electromagnetic noise (RF) of anthropogenic origin has been shown to disrupt magnetic orientation behavior in some animals. Two sources of natural RF might also have the potential to disturb magnetic orientation behavior under some conditions: solar RF and atmospheric RF. In this review, we outline the frequency ranges and electric/magnetic field magnitudes of RF that have been shown to disturb magnetoreceptive behavior in laboratory studies and compare these to the ranges of solar and atmospheric RF. Frequencies shown to be disruptive in laboratory studies range from 0.1 to 10 MHz, with magnetic magnitudes as low as 1 nT reported to have effects. Based on these values, it appears unlikely that solar RF alone routinely disrupts magnetic orientation. In contrast, atmospheric RF does sometimes exceed the levels known to disrupt magnetic orientation in laboratory studies. We provide a reference for when and where atmospheric RF can be expected to reach these levels, as well as a guide for quantifying RF measurements.

Appendices

Appendix A

In this appendix we explain the procedures typically used to quantify RF, provide guidance for converting between these methods, and summarize the methods used in this paper. As described below, electromagnetic fields are measured and quantified in different ways depending on whether they are narrowband or broadband.

‘Narrowband,’ or ‘single frequency’ RF spans a very small frequency range (Box 2). For narrowband RF, the magnitude of the electric or magnetic field is measured as either: (1) peak amplitude, or (2) Root-Mean-Square (RMS) amplitude. The relationship between an RMS amplitude and a peak amplitude depends on the waveform of the RF. For example, for a sinewave, peak amplitude = $\sqrt{2}$*RMS amplitude. While the relationship between peak and RMS amplitudes is known for all continuous, periodic waveforms, there is no such relationship for an arbitrary nonperiodic waveform. Because of this, most signal analyzers will report an RMS amplitude. For all data plotted in this review, RMS amplitude was used; however, often narrowband measurements are referred to simply as the “amplitude” or the “intensity” and no further information is given. In this case, we assumed the measurement was an RMS amplitude.

‘Broadband’ RF contains energy at many frequencies and often a continuum of frequencies (Box 2). Broadband RF is measured by dividing the overall frequency range into multiple frequency bins, and separate amplitude measurements are made for each bin. The amplitude measured within each bin will thus depend on the bin-size, or the resolution bandwidth of the measurement system (see Appendix B). In addition, the amplitude measured within each bin must then be integrated across time. Finally, to report a single magnitude measurement for broadband RF, one must integrate across the total frequency range. There are several ways to perform both of these integrations, many of which are noncomparable and can yield extremely different results. Because the magnetoreceptor is yet unknown, there is no way to determine which methods are most appropriate for quantifying how a magnetoreceptive animal perceives RF. Thus, it is imperative that any broadband study report their resolution bandwidth, methods of integration and provide a plot of the measured amplitude spectrum across frequencies. Without these details, it is not possible to convert between these different measurement methods. Here we summarize a few common integration methods across time and frequency for broadband RF:

Time: Broadband measurements cannot be taken instantaneously, and the amplitude at any one frequency will vary as the measurement is being taken. Most instruments integrate over time using either ‘average’ mode or ‘max-hold’ mode. The average mode computes the mean amplitude seen within each bin during the measurement duration, and the max-hold mode reports the maximum amplitude recorded within each bin at any point in time during the measurement duration. For white noise, and a sufficiently long measurement duration, average= $\sqrt{10}*$ max-hold (Kobylkov et al. 2019). All data plotted in this review were either made in average mode or converted to average mode using the conversion for white noise.

Frequency: Different researchers have used many different methods to integrate across their total frequency range, as summarized in (Kobylkov et al. 2019). For several reasons we recommend

$${B}_{\mathrm{RMS}}=\sqrt{\Delta f}\sqrt{\frac{1}{N}{\sum }_{i=1}^{N}{b}_{i}^{2}}$$

(1)

where, $\Delta f$ =total frequency range, N = number of bins integrated across, ${B}_{i}$ =the amplitude of each individual frequency bin, RBW = resolution bandwidth and $b_{i} = {\raise0.7ex\hbox{${B_{i} }$} \!\mathord{\left/ {\vphantom {{B_{i} } {\sqrt {{\text{RBW}}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sqrt {{\text{RBW}}} }$}}$ (Kobylkov et al. 2019). First, because it uses ${b}_{i}$ instead of ${B}_{i}$ it is not dependent on the resolution of the receiver (Appendix B). In other words, another measurement taken with a different resolution bandwidth will still yield the same result. In addition, ${B}_{RMS}$ is proportional to the square root of the power density and is the most comparable to the narrowband amplitude measurements. There are situations where other frequency-integration methods may be more appropriate, as discussed in (Kobylkov et al. 2019); however, it is not always possible to convert these integration methods directly. Thus, raw spectra should be included for all broadband measurements, along with the resolution bandwidths used, so that they can be re-integrated using a different method when required. For all broadband data plotted in this review, raw spectra were digitized from the original paper and converted into ${b}_{i}$ by dividing by the square root of the receiver resolution bandwidth and integrated using formula 1 above.

Appendix B

In this review, resolution bandwidth refers to the resolution of a measuring system, i.e., how finely the measuring device divides up the total frequency space of broadband RF before measuring the amplitude within each bin (Appendix A). In some papers, the term ‘bandwidth’ is used to refer to the total frequency range; however, the convention used in magnetoreception studies is to use ‘bandwidth’ to refer to the resolution of the measuring device. To avoid confusion, we thus use the term ‘resolution bandwidth.’ In this appendix, we report the ways in which to account for the resolution of a system for both broadband and narrowband RF (Box 2).

For broadband RF, this resolution has a significant impact on the amplitude reported by the measurement system. There are thus two options to fully specify the nature of the field. One is to provide a plot of the measured amplitude spectrum and also clearly specify the measurement resolution. If the measurement frequency resolution is not provided, then one cannot distinguish higher fields measured with a narrow frequency resolution from lower fields measured with a wide frequency resolution. The second option is to report the measured amplitude spectrum divided by the square root of the measurement resolution in Hz. This measurement is typically called a spectral density (Box 3) and yields a quantity that is independent of the measurement resolution.

For narrowband RF, the amplitude reported by the measurement system does not depend on the measurement resolution because increasing the measurement resolution bandwidth will not allow more energy into the measurement system. In this case, the first option of simply reporting the amplitude without the resolution bandwidth normalization is common. However, to eliminate any ambiguity, it is generally the best to report the resolution bandwidth and provide a spectrum for all RF types.