Techniques to determine the quiet day curve for a long period of subionospheric VLF observations

Very low frequency (VLF) transmissions propagating between the conducting Earth's surface and lower edge of the ionosphere have been used for decades to study the effect of space weather events on the upper atmosphere. The VLF response to these events can only be quantified by comparison of the observed signal to the estimated quiet time or undisturbed signal levels, known as the quiet day curve (QDC). A common QDC calculation approach for periods of investigation of up to several weeks is to use observations made on quiet days close to the days of interest. This approach is invalid when conditions are not quiet around the days of interest. Longer-term QDCs have also been created from specifically identified quiet days within the period and knowledge of propagation characteristics. This approach is time consuming and can be subjective. We present three algorithmic techniques, which are based on either (1) a mean of previous days' observations, (2) principal component analysis, or (3) the fast Fourier transform (FFT), to calculate the QDC for a long-period VLF data set without identification of specific quiet days as a basis. We demonstrate the effectiveness of the techniques at identifying the true QDCs of synthetic data sets created to mimic patterns seen in actual VLF data including responses to space weather events. We find that the most successful technique is to use a smoothing method, developed within the study, on the data set and then use the developed FFT algorithm. This technique is then applied to multiyear data sets of actual VLF observations.