S N Bentley

Parameterised (or statistical) models are being increasingly used in space physics, both as an efficient way to use large amounts of data and as an important step in real-time modelling, to capture physics on scales not incorporated in numerical modelling. We have used machine learning techniques to create a model for the power in ultra-low frequency (1-15mHz, ULF) waves throughout Earth’s magnetosphere. Capturing the power in these global-scale waves is necessary to determine the energisation and transport of high energy electrons in Earth’s radiation belts, and the model can also be used to test how individual wave driving processes combine throughout the magnetosphere.

The model is constructed using ensembles of decision trees (i.e. a random forest). Each decision tree iteratively partitions the given parameter space into variable size bins to reduce the error in the predicted output values. These variable bins mitigate several difficulties inherent to space physics data (sparseness, interdependent driving parameters, nonlinearity) to produce an approximation of ULF wave power in our chosen parameter space: physical driving parameters (solar wind speed vsw, magnetic field component Bz and variance in proton number density var(Np)) and spatial parameters of interest (magnetic local time MLT, magnetic latitude and frequency band).

It is not always possible to extract all physical processes from parameterised models such as this. Early applications of machine learning in space physics assumed that once a process was approximated with a set of parameters, all contributing processes could be extracted in terms of those processes. However, this is based on the false assumption of linearity between parameters and processes. Instead we suggest a hypothesis testing framework to examine the physics driving ULF wave power. This series of successive questions should use our existing knowledge to (a) state the process we think dominates, (b) hypothesise how the resulting wave power would manifest in the model, (c) test whether the model meets or contradicts our expectations, and (d) repeat, examining the remaining power for finer processes. This formalises the approach taken in full statistical surveys and makes clear that physics from parameterised models still fits clearly into the scientific method.

In the poster we demonstrate how this method of iteratively considering smaller scale driving processes applies to magnetic local time asymmetries in ULF wave power and to remaining uncertainty. The first example hypothesis tests under what conditions and locations a dawn-dusk asymmetry in power is observed. We conclude that:

• The dawn-dusk wave power asymmetry is a combined effect of the different radial density profiles and wave driving from magnetopause (or “external”) perturbations such as Kelvin-Helmholtz instabilities.
• We cannot account for the effects of a compressed magnetosphere, but var(Np) does not represent wave driving by magnetopause perturbations.
• Nor does Bz, which instead likely represents wave power increases with substorms.

The second example hypothesis tests where the remaining uncertainty is, or where the model characterises the physics least well. We suggested that this might be during substorms, i.e. when Bz<0. However, our results indicate that:

• Bz>0 has greater uncertainty. This is probably because there is larger variability in substorm occurrence for Bz>0 than Bz<0, so Bz<0 is a better hourly substorm proxy.
• Greatest remaining uncertainty is found for Bz>0, low vsw and low var(Np), i.e. when there is the least solar wind driving. This suggests that the configuration of the magnetosphere and internal processes are secondary effects that should be included in future.


Our model is freely available on Zenodo and our results are recently published in Earth and Space Science.