Characterization of the Ionospheric Vertical Error Correlation Lengths Based on Global Ionosonde Observations

Data assimilation is one of the most important approaches to monitoring the variations of ionospheric electron densities. The construction of the background error covariance matrix is an important component of ionospheric data assimilations. To construct the background error covariance matrix, the information about the spatial ionospheric correlations is required. We present a statistical analysis on the ionospheric vertical error correlation length (VCL) based on a global network of ionosondes and the Neustrelitz Electron Density Model. We show that the locally derived VCL is well-defined and the VCL does not show a considerable dependency on the geographical seasons while local time dependencies of the VCL are shown to be present. A novel VCL model is also established based on the ionospheric scale heights. We show that the ionospheric VCL can be characterized by the variance ratio between the ionosphere model and ionospheric measurements. The altitudinal variations of VCLs are controlled by the interactions between the inherent VCLs of the ionosphere model and the measurements. Two experiments are conducted at two different latitudes based on the proposed model. The results show that the proposed model is stable and well-correlated with the observed VCLs, which implies a potential to be generalized for a global correlation model. The proposed model can be used in the temporal evolution of error covariance matrices in the ionospheric 4D-Variational (4D-Var) assimilations, which may overcome the main drawbacks of the static error covariance specifications in the ionospheric 4D-Var assimilations.