FP models

Here, we detail the models used in parameter recovery. In previous FP work [33,30], low-order polynomials were sufficient to provide acceptably low reconstruction errors in the database. We follow this methodology and remark that in any model, the number of independent observations in the database should comfortably exceed (i.e. at least by a factor of two) the number of fitted parameters, thus we are constrained to models with less than about 200 parameters, preferably fewer. With these limitations in mind, and given the fact that investigations show that most parameters have a more complex dependence on predictors than a simple linear relation, we assume that the fitted models will be at least fully quadratic in the predictors (i.e. including first and second order terms plus all possible cross-combinations). The predictors used will consist of those determining the vacuum magnetic field ( $i_{\mathrm{s}}$, $i_{\mathrm{tor}}$ and $i_{\mathrm{vert}}$), the extent of the plasma ( ${Z_{\mathrm{lim}}}$) and the retained PCs of the magnetic signals to describe the plasma-induced deformation of the vacuum field.