Ionospheric vertical correlation distances: Estimation from ISR data, analysis, and implications 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 the 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 paper focuses on the vertical component of the model covariance matrix. Data from five different incoherent scatter radars (ISR) are analyzed to derive the vertical correlation lengths for the International Reference Ionosphere (IRI) 2016 model errors, because it is the background model for IDA4D. 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. The location and the magnitude of this bump are different for different radars. Solar flux binning introduces more pronounced changes in the correlation distances in comparison to magnetic local time (MLT) and seasonal binning of the data. The latitudinal distribution of vertical correlation lengths is presented and can be applied to the construction of the vertical component of the background model covariance matrix in data assimilation models that use IRI or similar empirical models as the background.