Abstract:  The total electron content (TEC) maps can be used to estimate the signal delay of GPS due to the ionospheric electron content between a receiver and a satellite. This delay can result in a GPS positioning error. Thus, it is important to monitor and forecast the TEC maps. However, the observed TEC maps have big patches of missingness in the ocean and scattered small areas on the land. Thus, precise imputation and prediction of the TEC maps are crucial in space weather forecasting.

In this talk, I first present several extensions of existing matrix completion algorithms to achieve TEC map reconstruction, accounting for spatial smoothness and temporal consistency while preserving important structures of the TEC maps. We call the proposed method video imputation with softImpute, temporal smoothing, and auxiliary data (VISTA). We show that our proposed method achieves better reconstructed TEC maps than existing methods in the literature. I will also briefly describe the use of our large-scale complete TEC database. Then, I present a new model for forecasting time series data distributed on a matrix-shaped spatial grid, using the historical spatiotemporal data and auxiliary vector-valued time series data. We model the matrix time series as an auto-regressive process, where a future matrix is jointly predicted by the historical values of the matrix time series and an auxiliary vector time series. Large sample asymptotics of the estimators are established, and performances of the model are validated with extensive simulation studies and a real data application to forecast the global TEC distributions.