Fractal Dimensions of Solar and Geomagnetic Indices
Abstract
Correlations between solar and geomagnetic indices are often used in space weather research. How sensitive are these correlations to pre-whitening of the data and auto-correlation within the data sets? Statistical and timeseries analyses of the sunspot number are often used to predict solar activity. These methods have not been completely successful as the solar dynamo changes over time and one cycle's sunspots are not a faithful predictor of the next cycle's activity. Can more accurate predictions be produced by partitioning the data into periods when it obeys certain statistical properties? The Hurst exponent and the related fractal dimension are two such ways to partition the data. We can use these measures of complexity to compare the sunspot number with other solar and geomagnetic indices. We use five algorithms to calculate the Hurst exponent or fractal dimension and examine what happens when the mean and a linear trend trends are removed. We find that some algorithms are robust and return similar or identical values for the original, mean-removed, and linear-trend-subtracted data. The behavior of the Fourier transform at low frequencies is the most sensitive to the type of pre-whitening applied to the data. The rescaled-range algorithm is robust but needs to be corrected for autocorrelation in the data.
- Publication:
-
American Astronomical Society Meeting Abstracts #234
- Pub Date:
- June 2019
- Bibcode:
- 2019AAS...23411801P