Ionospheric Horizontal Correlation Distances: Estimation, Analysis, and Implications for Ionospheric Data Assimilation

Abstract

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-today 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-today 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.

3‐D Regional Ionosphere Imaging and SED Reconstruction With a New TEC‐Based Ionospheric Data Assimilation System (TIDAS)

“…Forsythe et al. (2020, 2021) constructed global maps of ionospheric correlation lengths and developed new background covariance models for ionospheric data assimilation. These avenues provide a useful step toward improving the specification of background error covariance. Devising high‐precision regional data assimilation schemes to specify detailed localized ionospheric weather features: Most current ionospheric data assimilation models have been built to run on a global scale that may not always have optimal performance in representing local mesoscale ionosphere morphology.…”

“…Recently, some studies used hybrid assimilation approaches to combine the merits of variational methods and ensemble-based algorithms (e.g., Schwartz et al, 2014;. Forsythe et al (2020Forsythe et al ( , 2021 constructed global maps of ionospheric correlation lengths and developed new background covariance models for ionospheric data assimilation. These avenues provide a useful step toward improving the specification of background error covariance.…”

Data Assimilation Retrieval of Electron Density Profiles From Ionosonde Virtual Height Data

“…This technique, however, is not ideal in case the VH data needs to be assimilated together with other data sources. For the data assimilation schemes, such as Ionospheric Data Assimilation Four‐Dimensional (IDA4D) (Bust et al., 2001, 2004; Bust & Datta‐Barua, 2014; Forsythe, Azeem, & Crowley, 2020), it is important to be able to assimilate all the data points within one time frame together. Figure 8 compares the results of sequential and simultaneous VH data ingestion.…”

“…For retrieval of the electron density from VH data, only the vertical direction is considered, making it a 1‐D problem. Typically, to model the vertical component of the covariance matrix an assumption is used that the vertical correlations are represented by a Gaussian (Aa et al., 2015, 2016; Bust & Crowley, 2007; Bust & Datta‐Barua, 2014; Bust et al., 2001, 2004; Coker et al., 2001; Forsythe, Azeem, & Crowley, 2020; Forsythe et al., 2021; Yue et al., 2007, 2011). The construction of the error covariance matrix can be separated into the construction of two matrices: the model variance matrix and the vertical correlation matrix .…”

The Global Analysis of the Ionospheric Correlation Time and Its Implications for Ionospheric Data Assimilation

“…Many investigations have explored the spatial correlation distances of the ionosphere. For example, horizontal correlation distances have been studied using TEC data (Forsythe, Azeem, & Crowley, 2020; Gail et al, 1993; Klobuchar et al, 1995; Shim et al, 2008; Yue et al, 2007), and vertical correlation distances have been investigated using Incoherent Scatter Radar (ISR) data (Forsythe, Azeem, Crowley, & Themens, 2020; Yue et al, 2007). To the best of our knowledge, no previous investigations have examined in detail the temporal ionospheric correlation or the relaxation parameter.…”