Ionospheric horizontal correlation distances: Estimation, analysis, and implications for ionospheric data assimilation

The background covariance matrix establishes the transition from the data- to model-driven regions in the ionospheric data assimilation algorithms. To construct the background covariance matrix, the information about the spatial ionospheric correlations of model errors is required. This paper focuses on the horizontal component of the covariance matrix. It is the first study that presents global maps of zonal and meridional ionospheric correlation lengths derived for IRI-2016 model errors. The model errors were calculated using 20 years of GPS total electron content (TEC) values from the Jet Propulsion Laboratory Global Ionospheric Maps (GIMs) for different seasons, geomagnetic conditions, and universal times. The correlation lengths derived from IRI model errors were analyzed and compared to correlation lengths derived from day-to-day ionospheric variability calculated from GIM. It was found that the global distributions of the zonal and meridional correlation lengths between the two approaches are very different and that the correlation lengths derived from day-to-day TEC variability cannot be used as a proxy for the construction of covariance matrix for ionospheric data assimilation. A new method is proposed for the modeling of azimuthal distribution of the correlation distances that considers the nonisotropic nature of the distribution of correlations around the reference point.