Abstract: Twenty-first century life is highly dependent on satellite services, which are at risk from the hazardous radiation belt environment. Ultra-low frequency waves (ULF, 1-10 mHz) are large-scale plasma waves, predominantly driven by the solar wind. These waves are responsible for the radial transport and energisation of electrons in Earth's radiation belt, and are therefore essential components of radiation belt modelling. Current models of ULF waves and the resulting radial diffusion are deterministic, producing a single output for each set of input parameters.  

Meanwhile, probabilistic modelling is used heavily in weather and climate models to improve forecasting. These methods capture some of the uncertainty inherent in a complex system, accounting for the effects of sub-scale processes and accurately representing the full range of possible physical states more faithfully than by solely using the mean or median. We aim to apply these methods to better determine the impact of ULF waves on Earth’s radiation belts. 

By considering a parameterisation as an approximation of a manifold in our parameter space, we find that random forests (a machine learning technique) inherently have the properties for an empirical model which should mitigate typical space physics data issues such as sparseness, interdependence and nonlinearity. Our new, freely available model is presented and we motivate the idea of iterative hypothesis testing as a method of extracting physics from nonlinear empirical models. We examine the magnetic local time variation of ULF wave power and find that remaining uncertainty in the model suggests we need to capture the internal state of the magnetosphere for future models.