Constraining solar wind transport model parameters using Bayesian analysis

Abstract

We apply nested-sampling (NS) Bayesian analysis [AshtonEA22] to a model for the transport of MHD-scale solar wind fluctuations. The dual objectives are to obtain improved constraints on parameters present in the turbulence transport model (TTM) and to support comparisons of distinct versions of the TTM. The TTMs analysed are essentially 1D steady-state presented in [BreechEA08] that describe the radial evolution of the energy, correlation length, and normalized cross helicity of the fluctuations, together with the proton temperature, in prescribed background solar wind fields. Modelled effects present in the TTM include nonlinear turbulence interactions, shear driving, and energy injection associated with pickup-ions. These effects involve adjustable parameters that we seek to constrain. Bayesian analysis supports the efficient searching of a parameter space for the 'best' set of TTM parameter values. More advanced use provides the parameter's posterior distribution: its probability given the data, and the model. This can be used to understand the uncertainty in the provided 'best' values for the parameters and therefore the uncertainty in the suggested TTM solutions/predictions. By using NS, we can calculate the Bayesian evidence for each TTM and objectively determine which best fits the given observational data. Based on the analysis of the datasets and TTM employed, we recommend use of the 2D TTM with von Karman-Howarth parameters ${\alpha}\approx 0.16$ and $\beta \approx 0.10$ and parameter assumptions from existing literature. It is important to include the pickup ion effects in the lengthscale evolution equation by assuming $Z^{2\beta/\alpha}\lambda = const$ is locally conserved. This work is readily extended to more sophisticated solar wind models. Although more work is required to generate datasets with associated errors, which is necessary for accurate Bayesian modelling.