Data Assimilation for the Two-Dimensional Ambipolar Diffusion Equation in Earth’s Ionosphere Model

V. P. Dymnikov; Дымников В. П.; D. V. Kulyamin; Кулямин Д. В.; P. A. Ostanin; Останин П. А.; V. P. Shutyaev; Шутяев В. П.

doi:10.31857/S0044466923050101

Data Assimilation for the Two-Dimensional Ambipolar Diffusion Equation in Earth’s Ionosphere Model

Authors: Dymnikov V.P.¹^,2, Kulyamin D.V.¹^,2, Ostanin P.A.¹^,3, Shutyaev V.P.¹^,3
Affiliations:
1. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences
2. Fedorov Institute of Applied Geophysics
3. Moscow Institute of Physics and Technology (National Research University)
Issue: Vol 63, No 5 (2023)
Pages: 803-826
Section: МАТЕМАТИЧЕСКАЯ ФИЗИКА
URL: https://journals.rcsi.science/0044-4669/article/view/136138
DOI: https://doi.org/10.31857/S0044466923050101
EDN: https://elibrary.ru/GFURSG
ID: 136138

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Abstract
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Abstract

The problem of variational data assimilation for the INM RAS two-dimensional diffusion model of the Earth’s ionosphere F region is considered. Total integral electron contents along given paths are used as observation data. The general statement of the problem in differential form is formulated, and its solvability is analyzed. Based on a regularized statement, an iterative algorithm for solving the assimilation problem is constructed, and its convergence is demonstrated. A finite-dimensional approximation is constructed, the numerical solution of the problem is implemented, and the stability and convergence of the difference scheme are proved. The quality of the reconstruction of electron concentration fields is examined in test numerical experiments. It is shown that a weakly perturbed solution is reconstructed with acceptable accuracy for both stationary and evolutionary statements in the case of vertical and slant integration paths.

Keywords

ionosphere, ambipolar diffusion, inverse problems, variational data assimilation, numerical simulation

References

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