Determination of the Signal Fluctuation Threshold of the Temperature-Ion Composition Ambiguity Problem Using Monte Carlo Simulations

Unambiguously estimating the plasma parameters of the ionosphere at altitudes between 130 and 300 km presents a problem for the incoherent scatter radar (ISR). At these ranges, ISR is unable to distinguish between different mixtures of molecular ions (NO+ and O-2(+)) and atomic oxygen ions (O+). Common solutions to this problem are either to employ empirical or theoretical models of the ionosphere or to add a priori known plasma parameter information obtained from the plasma line of the ISR spectrum. Studies have demonstrated that plasma parameters can be unambiguously estimated in almost noiseless scenarios, not commonly feasible during routine monitoring. In this study, we define a theoretical framework to quantify the ambiguity problem and determine the maximum signal fluctuation levels of the ISR signal to unambiguously estimate plasma parameters. We conduct Monte Carlo simulations for different plasma parameters to evaluate the estimation performance of the most commonly used nonlinear least squares optimization algorithm. Results are shown as probability curves of valid convergence and correct estimation. We use simulations to quantify the estimation error when using ionospheric models as initial conditions of the optimization algorithm. We also determine the contribution to the estimation process of different combinations of parameters known from the plasma line, the particular contribution of each plasma parameter, and the effect of increasing the level of uncertainty of the parameters known a priori. Results suggest that knowing a priori both electron density and electron temperature parameters allows an unambiguous estimation even at high fluctuation levels.