Techniques to Determine Quiet Day Curves for Subionospheric VLF Observations

Abstract

The ionization rate of the upper atmosphere can be significantly increased by space weather events, examples being solar proton events (SPE), solar flares, and energetic electron precipitation from the radiation belts. An increase in the ionization rate leads to a lowering of the lower edge of the ionospheric D-region. To study the effect of space weather events on our atmosphere it is important 1) to be able to detect the events and also 2) to have some way of determining changes in the height of the D-region. Very low frequency (VLF) radio waves propagate in the waveguide between the surface of the Earth and the lower edge of the ionosphere (D-region). Changes in the height of the D-region lead to changes in the amplitude and phase of the VLF signal received at an antenna. To gain an accurate indication of the size of these changes we need to know what the undisturbed signal, known as a Quiet Day Curve (QDC), would have been if no space weather event had taken place.

High power narrow-band communications transmitters operated by multiple nations provide the VLF radio signals used in this technique. In this study we use VLF radio wave observations from the Antarctic-Arctic Radiation- belt Dynamic Deposition VLF Atmospheric Research Konsortia (AARDDVARK) receivers located at Edmonton, Canada and Scott Base, Antarctica.

The purpose of this study is to develop a technique for the automatic calculation of QDCs for long-period experimental subionospheric VLF data sets. To enable the quantitative evaluation of how well our QDC finding techniques identify the true QDC of a data set, we have created a suite of synthetic data layers with a known QDC and imposed perturbations similar to those seen in real VLF data. We present this evaluation and comparison between the techniques to allow determination of the best QDC finding technique from those developed.

We evaluate two techniques for determining a long-period QDC by algorithm. These are Principal Component Analysis (PCA) and 2-dimensional Discrete Fourier Transforms (DFT). We also evaluate an averaging technique that finds a combined daily curve as a baseline comparison to our techniques. We further evaluate several adjustments to these techniques, endeavouring to improve the resulting QDC. We determine that the best QDC technique for data sets longer than two years is an adjustment to the DFT technique, while, for data sets shorter than two years, the best technique is PCA applied to a smoothed data set.

We judge the success of our adjusted DFT technique from the finding that the typical difference between the QDC and the synthetic data background is 0.13~dB for day and 0.17~dB for night. These values are smaller than typical experimentally observed noise levels. We therefore conclude that this QDC finding technique is successful. The pre-smoothed PCA technique gives a typical difference between the QDC and the synthetic data background of 0.38~dB for day, 0.47~dB for night. We therefore conclude that this QDC finding technique is fairly successful, although not as conclusively as the DFT based technique is.

We then apply our chosen QDC finding techniques, according to the length of the data sets, to the VLF observations. We apply the adjusted DFT technique to our Scott Base data sets, which span 4 years of observations, i.e., 2,103,840 minutes. We find that the QDC finding technique appears to qualitatively extract the QDC from these real data sets. In particular during solar flares, the extraction looks sensible. We provide examples of the difference between the received VLF signal and the QDC for an example day during which 10 solar flares occurred. We apply the pre-smoothed PCA technique to our Edmonton data sets, which span 20 months of usable data, i.e., 915,840 minutes. We find that this technique appears to be working, but have less confidence in its ability to extract perturbations lasting longer than a few hours.