Revisiting ISR Spectra Modeling: Higher-Order Stochastic Approach and Surrogate Models

The Incoherent Scatter Radar (ISR) technique is the most used in ground-based radars for ionospheric plasma parameter estimation. Based on single-particle statistics and a nonlinear Langevin equation, Milla and Kudeki (2011) develop a new model that considers the physics of Coulomb collision. Nevertheless, the computational limitations and low simulation efficiency of the Euler-Maruyama scheme motivates the use of a higher-order stochastic algorithm. In this work, a broad exploration about SDE algorithms was performed, considering the adaptive time-step solvers. These new schemes will be compared to the previously developed solver by Milla and Kudeki [1], focusing on the precision of moment estimations, and computational efficiency, as observed in the weak convergence analysis. Furthermore, a decoupling metric for perpendicular and parallel directions of the displacement’s characteristic functions is displayed for a reduced plasma parameter space. Finally, recent data-driven efforts to extend the closed-form solution for the spectra is described. This includes using composite distribution functions to capture deviations from Gaussianity in the distribution of particle displacements parallel to Earth’s magnetic field, as well as the potential for Gaussian processes to capture the ISR autocorrelation functions in equilibrium conditions.