Analysis of local ionospheric time varying characteristics with singular value decomposition

In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations in Denmark located in the midlatitude region.

The station separation between the three stations is 132–208 km (the time series of the TEC can be freely downloaded at http://www.heisesgade.dk). For each year, a SVD has been performed on the TEC time series in order to identify the three time varying (daily, yearly, and 11 yearly) characteristics of the ionosphere.

The applied SVD analysis provides a new method for separating the daily from the yearly components. The first singular value is very dominant (approximately six times larger than the second singular value), and this singular value corresponds clearly to the variation of the daily cycle over the year.

The second singular value corresponds to variations of the width of the daily peak over the year, and the third singular value shows a clear yearly variation of the daily signal with peaks around the equinoxes. The singular values for each year show a very strong correlation with the sunspot number for all the singular values.

The correlation coefficients for the first 5 sets of singular values are all above 0.96. Based on the SVD analysis yearly models of the TEC in the ionosphere can be recomposed and illustrate the three time varying characteristics of the ionosphere very clearly. By prediction of the yearly mean sunspot number, future yearly models can also be predicted.

These can serve as a priori information for a real time space weather service providing information of the current status of the ionosphere. They will improve the Kalman filter processing making it more robust, but can also be used as starting values in the initialization phase in case of gaps in the data stream.

Furthermore, the models can be used to detect variations from the normal local ionospheric activity.