Analysis of the Rhode Island

Schumann Resonance Daily-Average Data

 

XV International Conference on Atmospheric Electricity, 15-20 June 2014, Norman, Oklahoma, U.S.A.
Robert Boldi
College of Sustainability Sciences and Humanities, Zayed University, Dubai, United Arab Emirates

Earle Williams
Parsons Laboratory, Massachusetts Institute of Technology, Cambridge Massachusetts, USA.

Anirban Guha
Tripura University, Tripura, India.

ABSTRACT: A variety of putative influences upon Schumann resonance (SR) signals have been evaluated
for the case of a 20 year record of measurements of two magnetic-field detectors and one electric-field
detector located at West Greenwich Rhode Island, U.S.A. (71.6W, 41.6N). The detector-specific SR signals
considered are the values of the parameters of the first six modes of an eight-mode, three-parameter,
Lorentzian-line-shape model. The three parameters of the model are peak-center frequency, peak-quality
factor, and peak intensity. This model was used to fit the daily-average Fourier-transform intensity spectra
spanning the frequency range 3 Hz - 56 Hz. This results in 54 SR signals: 3 channels 6 modes / channel
3 parameters / mode.
We also computed an expected climatological-daily-average intensity spectra for each day and detector
and fit these spectra to the above mentioned Lorentzian model. A linear regression of the observed parameters
to the expected parameters finds that on average the climatological-daily-average data account for
35% of the variance (R2 = 0.35) of the original SR series, with the best fits obtained for the Lorentzian-fit
parameter peak-intensity where 70% of the variance of the original series was explained. Averaging across
channels and parameters, the second and third modes were best modeled by the climatological-average data,
explaining 50% of the total variance; all above results are significant at the p 0:001 level.
We then subtracted the observed SR signals from the expected SR signals to generate residual SR signals.
The residual SR time series display a systematic variation following the 11-year sunspot cycle. A linear
regression of a nominal sunspot cycle with the residual time series averaged across all modes and channels,
finds R2 values for peak-center frequency = 0.59, peak-quality factor = 0.31, and peak intensity = 0.0.
Averaging the residual time series across all modes and fit parameters, the sunspot cycle is found in each
channel; the R2 value for the E/W channel = 0.30, the R2 for the N/S channel = 0.37, and the R2 value for
the Ez channel = 0.24 The sunspot-cycle pattern is strongest the mode 1 data (R2 = 0.48) and decreases with
increasing mode number; the R2 for mode 6 = 0.15; all significant at the p 0:001 level.
We then examined various putative influences upon these residual SR signals using a variety of techniques.
The results indicate that direct measures of solar activity (e.g. sunspot number and area) most
strongly influence peak-center frequency and peak-quality factor (median R2 = 0.50) and less so the peakintensity
(median R2 = 0.02). Terrestrial temperature signals (e.g. Ocean temperature anomalies) influence
peak-intensity (median R2 = 0.15) but not peak-center frequency nor peak-quality factor (median R2 =
0.01).
We also examined the spectral characteristics of the residual SR signals. Both the peak-center frequency
and peak-quality factor parameters, averaged over all of the modes and channels, display strong peaks at
11 years, 365 days, 180 days; in contrast, the peak-intensity parameter displays no similar features. This
indicates that the values of the peak intensity parameter are well predicted by the global total lightning and
the uniform-cavity model, while the peak-center frequency and peak-quality factor parameters are not. The
values of these two parameters have a significant variation over the sunspot cycle unaccounted for by the
global total lightning and the uniform-cavity model.

 

1 INTRODUCTION
The intent of this paper is to determine the causes of the temporal fluctuations observed in the the
Schumann resonance (SR) signals recorded at West Greenwich, Rhode Island, U.S.A. (71.6W, 41.6N).
While previous authors (e.g. Shvets et al [2010], Nickolaenko et al [2011], Williams and Satori [2007],
Williams et al [2006], and Williams et al [2010] ) have used subsets of this data set, we here report on the
data in its entirety in order to place earlier results in the context of the entire data set. We limit this analysis
to those fluctuations occurring over periods of a day or longer; in a forthcoming paper we will examine
the fluctuations occurring on periods of less than a day. The method we used to examine the temporal
fluctuations is summarized as follows and is explained in detail in the subsequent sections.
We transformed the time series into two-minute-average Fourier-transform spectra and from these
spectra computed the observed daily-average Fourier-transform spectra. Our nominal expectation is that
these time series primarily represent the diurnal and annual variations in global lightning activity. In addition,
we expect that the Fourier-transform intensity spectra of these time series, on short time periods
(10’s of seconds), are dominated by a few large-amplitude events. These events come from a variety of distances,
and consequently, averaging the short term spectral intensities into a daily-average intensity spectra
should reflect the diurnally-averaged distribution of distances to large events. We note that these spectra
quite different from that obtained by computing a single Fourier transform of single time series 24 hours in
duration.
We then computed the expected daily-average spectra and fit both the observed and expected spectra
to an eight-mode, three-parameter Lorentzian spectral model. The three parameters of the model are peakcenter
frequency, peak-quality factor, and peak intensity. We retain the first 6 modes for analysis; this
resulted in a set of 54 time series of fit parameters: 3 channels 6 modes / channel 3 parameters / mode.
We subtracted the expected time series from the observed time series for each of the 54 time series; this
produced the residual or unexplained variation in the SR signals. We compared these residuals with variety
of putative influences using various methods. These steps are detailed below. Finally, we present a summary
of our findings and conclusions.
 

THE RHODE ISLAND TIME SERIES
The SR signals studied here originated as three independent time series, each generated by one of
three independent recording systems operating at a sampling rate of 350 Hz (during 1992 – 2006) and at
4 kHz (from 2006 – present). These detectors sample the vertical electric field and the North/South and
East/West components of the horizontal magnetic field as described in Heckman et al [1998].
Data processing began by sliding a 15-second-wide Hann window over the data, if the data in the
window were complete, had no clipped values, and had a RMS value that was within nominal limits, then
the data were accepted as valid. During periods of background noise at Rhode Island, when the noise was
characterized as a set of line-interferences, this Hann window was increased to 30 seconds to improve the
spectral resolution and assist in detecting and removing the line interferences.
Of the approximately 7,000 days in the study period, we obtained approximately 3,000 days of data,
with 600 runs of good data averaging 5 days in length. Some of the data breaks were due to long periods
of local anthropogenic noise causing the time series and spectra to fail the various data quality checks, and
some breaks in the data were to instrumental failures of various types (mostly caused by nearby lightning
strikes).
 

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