Gap Filling of Solar Wind Data by Singular Spectrum Analysis


Solar wind and interplanetary magnetic field (IMF) data have large gaps before the launch of the WIND spacecraft in 1994. Singular spectrum analysis (SSA) can reconstruct missing data by using an iterative algorithm which infers coherent spatio-temporal  “signal” modes, while  discarding the “noise” (Kondrashov and Ghil, 2006). Here the gaps of the solar driver (such as solar wind parameters and IMF) are filled-in by smooth modes of co-variability with the continuous response (geomagnetic indices such as AE,Kp and Dst), as captured by the multivariate-SSA (Kondrashov et al. 2010).

As a proof-of-concept and to find optimal SSA parameters we demonstrate here SSA reconstruction performed over the full solar cycle (~4400 days) in the synthetic gaps for IMF Bz and dynamic pressure P. The synthetic gaps are created in the 1996-2007 hourly solar wind data data by applying gaps existing in 1972-1983. The gappy solar wind parameters  are then combined separately with time-continuos geomagnetic indices (AE, Kp, and Dst) to form multivariate dataset of four time series to which SSA is applied. Such synthetic experiment allows to tune optimal parameters of SSA algorithm (temporal window M and number of modes K) when reconstructing realistic gaps,  and assess the resulting reconstruction skill.

In the figures below we show an optimal SSA reconstruction for Bz and dynamic pressure in the synthetic gaps (marked by thick black lines along x-axis in panels for Bz and dynamic pressure). and compare it with validation time series in 1996-2007. Also shown are time-continuous geomagnetic indices.  The optimal SSA reconstruction that results in best reconstruction skill has been obtained by using temporal window M=20 hours and leading K=8 modes from the total number of 4x20=80 SSA modes.  The solar wind data is reconstructed in large gaps with realistic variability and high fidelity for large variety of geomagnetic conditions and gap sizes: the overall reconstruction skill in the gaps for Bz is 0.68 in correlation, and 0.74 in normalized root-mean-squared error (RMSE); for dynamic pressure it is 0.87 in correlation, and 0.48 in normalized RMSE. The skill for dynamic pressure is better as it is mostly Bz south that is captured in the reconstruction, as expected.

To inspect these results in details click on the images below and then use download option.


Kondrashov, D., R. Denton, Y. Y. Shprits, and H. J. Singer, 2014:

Reconstruction of gaps in the past history of solar wind parameters,

Geophys. Res. Lett., 41, 2702–270, doi:10.1002/2014GL059741.

  1. Kondrashov, D., Y. Shprits, M. Ghil, 2010:

Gap Filling of Solar Wind Data by Singular Spectrum Analysis,

Geophys. Res. Lett, 37, L15101, doi:10.1029/2010GL044138.

  1. Kondrashov, D. and M. Ghil, 2006:

Spatio-temporal filling of missing points in geophysical data sets,

Nonlin. Processes Geophys., 13, 151-159, doi:10.5194/npg-13-151-2006

  1. Data source: OMNIWEB

  1. Reconstruction for Radiation Belts and Wave Modeling Group

This research has been funded by National Science Foundation Award AGS-1102009

SSA gap-filling algorithm is applied to existing gaps in solar wind data using optimal SSA parameters that are obtained after testing on synthetic gaps. Gaps are filled for for 1972-Oct. 2013 data with hourly resolution: IMF components By, Bz, proton density Np, Alpha/proton ratio Na/Np, solar wind speed Vsw, and dynamic pressure P (see OMNI data set convention)

Both reconstruction datasets and results of testing with synthetic gaps are available by following the link below as  zipped archives (6-20Mb).

This data is also available online in SI of Kondrashov et al. 2014 GRL paper.