In ionospheric tomography, the atmospheric electron density is reconstructed from different electron density related measurements, most often from ground-based measurements of satellite signals. Typically, ionospheric tomography suffers from two major complications. First, the information provided by measurements is insufficient and additional information is required to obtain a unique solution. Second, with necessary spatial and temporal resolutions, the problem becomes very high dimensional, and hence, computationally infeasible. With Bayesian framework, the required additional information can be given with prior probability distributions. The approach then provides physically quantifiable probabilistic interpretation for all model variables. Here, Gaussian Markov random fields (GMRFs) are used for constructing the prior electron density distribution. The use of GMRF introduces sparsity to the linear system, making the problem computationally feasible. The method is demonstrated over Fennoscandia with measurements from global navigation satellite system (GNSS) and low Earth orbit (LEO) satellite receiver networks, GNSS occultation receivers, LEO satellite Langmuir probes, and ionosonde and incoherent scatter radar measurements.

We present a novel ionospheric tomography reconstruction method. The method is based on Bayesian inference with the use of Gaussian Markov random field priors. We construct the priors as a system of stochastic partial differential equations. Numerical approximations of these equations can be represented with linear systems with sparse matrices, therefore providing computational efficiency. The method enables an interpretable scheme to build the prior distribution based on physical and empirical information on the structure of the ionosphere. We show through synthetic test cases in a two-dimensional setup of latitude-altitude slices how this method can be applied to satellite-based ionospheric tomography and how information about the structure of the ionosphere can be implemented in the prior. The technique is capable of being easily extended to multifrequency tomographic analysis or used for the inclusion of other data sets of ionospheric electron density, such as ground-based observations by radars or ionosondes.

We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.

Whitepaper #294 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: space weather applications; basic research. Additional topics: space weather research/applications/operations pipeline; planetary ionospheres / upper atmospheres; other […]