Bayesian Inference of Quasi-Linear Radial Diffusion Parameters using Van Allen Probes

The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is derived from a quasi-linear approach with prescribed inner and outer boundary conditions. The 1D diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which is typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (e.g., Kp). These terms are typically empirically derived, not directly measurable, and hence are not known precisely, due to the inherent nonlinearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the empirical parameterization employed in the literature. Key Points We present the first application of Bayesian parameter estimation to the problem of quasi-linear radial diffusion in the radiation belt The Bayesian approach allows the problem to be cast in probabilistic terms and for ensemble simulations to be run An improved accuracy is demonstrated when compared against standard deterministic models