Tailoring of EOFs for Ionospheric Tomography and the Weighted, Partitioned, Least-Squares Algorithm

Abstract

Among the linear-algebraic class of inversion techniques used for ionospheric tomography is the Weighted, Damped, Least-Squares (WDLS) algorithm. One application of it uses empirical orthogonal functions (EOFs) as a vertical basis set and Fourier harmonics horizontally. To date, the EOFs employed have been generated from a large database of electron-density profiles with the intent of spanning all ionospheric states. In this work, we explore the utility of tailoring the EOFs for specific ionospheric conditions by limiting their span in latitude, longitude, local time, season, solar epoch, and geomagnetic disturbance level. In this paper, we demonstrate early results, showing some improvement by tailoring in latitude. We also describe a successor to the WDLS method, the Weighted, Partitioned, Least-Squares (WPLS) algorithm, which combines weighting with the partitioning capability of singular-value decomposition (SVD). In particular, we introduce a simple criterion for truncating the SVD series of singular values.