The importance of the covariance model for ionospheric data assimilation.

The construction of the background covariance matrix is an important component of ionospheric data assimilation algorithms, such as Ionospheric Data Assimilation Four-Dimensional (IDA4D). It is a matrix that describes correlations between all the grid points in the model domain and determines the transition from the data-driven to model-driven regions. The vertical component of this matrix also controls the shape of the assimilated electron density profile. To construct the background covariance matrix, the information about the spatial ionospheric correlations is required. This presentation focuses on the vertical component of the model covariance matrix. Data from five different Incoherent Scatter Radars is analyzed to derive the vertical correlation lengths for International Reference Ionosphere 2016 model errors. The vertical distribution of the correlations is found to be asymmetric about the reference altitude around which the correlations are calculated, with significant differences between the correlation lengths above and below the reference altitude. It is found that the correlation distances not only increase exponentially with height, but also have an additional bump-on-tail feature. Several experiments were conducted to assess performance of IDA4D with data-driven vertical covariance matrices. We show that the vertical part of the covariance model plays very important role because it preserves the vertical structure of the F-region density layer and helps to correct a tomographic issue that arises when the slant total electron content (sTEC) is assimilated along the intersecting rays. The results show that the new covariance model improves the fidelity of IDA4D algorithm, making it more suitable for the regional assimilation with dense ground-based Global Positioning System (GPS) data coverage.