The Four‐Dimensional Variational Neustrelitz Electron Density Assimilation Model: NEDAM

Abstract

It is of particular interest to retrieve the electron density distribution from Global Navigation Satellite System (GNSS) observations due to its high density and broad spatial-temporal coverage. There are several commonly used methods such as Computerized Ionospheric Tomography (CIT), Bayesian analysis and Kalman filter (Bust et al., 2001;Prol et al., 2021;Scherliess et al., 2004). However, different methods differ in many aspects including computational cost, data storage and management cost, compatibility for different kinds of observations and flexibility in practical applications.Several different techniques are developed to perform posterior analyses of the ionospheric electron density. One of the traditional techniques is CIT. CIT is a direct inversion technique that develops a two-dimensional electron density specification from a series of one-dimensional ionospheric observations and various minimization criteria (Kronschnabl et al., 1997;Raymund, 1995;Raymund et al., 1994). Similar work by other groups have led to the development of more advanced spatial analysis techniques. Howe et al. (1998) developed a Kalman filter method for ionospheric reconstruction based on spherical harmonics and Empirical Orthogonal Function describing the horizontal and vertical distribution, respectively. Manuel Hernández-Pajares et al. (1999, 2002)

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

“…The Gaussian correlation function is frequently used in various ionospheric data assimilation tools (Bust et al, 2004;Forsythe, Azeem, Blay, et al, 2021;Ssessanga et al, 2018). For example, in the Gaussian-Markov random field approximation of the precision matrix in NEDAM, the correlation lengths serve as scaling factors in the finite-difference matrix (Yuan et al, 2023).…”

“…Each sub-model is driven by the solar radio flux index F10.7 and the 3D global outputs are realized by combining multiple Chapman layers with a superposed exponential decay function describing the plasmasphere. Apart from NEDM, a new assmilative model NEDAM was recently developed based on a 4D-Variational (4D-Var) approach by Yuan et al (2023). The background electron density model NEDM may contain the climatological variation of the ionosphere while the assimilation NEDAM refines the background model with the short-term variations.…”

“…Although the detailed strategies among all assimilation tools may differ, one of the main challenges of data assimilations is the lack of knowledge about the error covariance information of the background model. The correlations among ionospheric electron densities are not only important for a better understanding of the ionospheric physical processes which determine the behavior of ionosphere but also an essential part in the data assimilations (Daley, 1991;Scherliess et al, 2006;Shim et al, 2008;Yuan et al, 2023). estimate the background error covariances via the ensemble method (Codrescu et al, 2018;Kodikara et al, 2021;Yue, Wan, Liu, & Mao, 2007;Yue, Wan, Liu, Zheng, et al, 2007).…”

“…Data assimilation is one of the most important approaches to monitoring the variations of ionospheric electron densities. During the past two decades, several assimilation tools were developed, such as the Ionospheric Data Assimilation Four-Dimensional (IDA4D), Global Assimilative Ionospheric Model (GAIM (Bust & Crowley, 2007;Bust & Datta-Barua, 2014;Bust & Mitchell, 2008;Bust et al, 2004) and Neustrelitz Electron Density Assimilative Model (NEDAM) (Yuan et al, 2023). Although the detailed strategies among all assimilation tools may differ, one of the main challenges of data assimilations is the lack of knowledge about the error covariance information of the background model.…”

“…But at the same time, large correlations especially in the peak density regions prevent the change of peak density heights. It is also suggested that the intersected observations need to be weighted properly by introducing the non-zero off-diagonal terms in the observation covariance matrice (Yuan et al, 2023). Forsythe, Azeem, Crowley, and Themens (2021) evaluated the vertical error correlation length (VCL) of electron densities based on a statistical analysis using IRI2016 and 5 operational incoherent scatter radar (ISR) stations.…”