Example of a type I spectrum that shows two ranges of scaling within the IR with an exponent close to IK at higher frequencies (blue circles in the top panel) and a shallower range at lower frequencies (green circles in panel a). There is a transition ‘1/f’ scaling at the lowest frequencies (black triangles in panel a). The interval is for PSP/FIELDS measurements of the full trace of the power spectral tensor, taken over a 48 h interval at 0.17 AU with local plasma β = 0.34. (a): Log-log plot of PSD versus frequency. The plotted points result from a Haar wavelet analysis of the dataset. (b): Procedural diagram for the four plots used to identify the breakpoints between three scaling ranges and their best-fit gradients. Breakpoints at the point labelled Q (between gradients –1.52 and –1.25) and the point labelled R (between IR gradient –1.25 and ‘1/f’; the latter terminates at the point labelled T) were identified from the CI of the exponent using the method outlined in Sect. 2.2 and are displayed in panels c to f. (c): Minimum exponent CI located at the point labelled Q for pathway (i) extending from point 3 upwards (blue). The continuation of the pathway (i) beyond point 8 suggests a second breakpoint at point 12, where the CI suddenly increases. (d): Pathway (ii) descending from point 8 (yellow). It has a minimum CI when it encompasses points down to the third scale. (e): Exponent and CI for pathway (iii), in green. This confirms the breakpoint at the point labelled R. (f): Exponent and CI for pathway (iv), showing that the ‘1/f’ range continues to the point labelled T.