Ionospheric diagnostics come from in-situ probes carried by rockets or satellites, forward propagation, and radar backscatter. This blog entry addresses in situ measurements and remote sensing via forward radio propagation from satellite to ground propagation paths. In situ measurements are time series generated the probe trajectory through the three-dimensional ionospheric structure. Propagation measurements are one-dimensional scans of a diffraction field that responds to the cumulative structure along the propagation path from the source to the receiver. The one-dimensional measurements are highly non-stationary with a very large range of contributing scale sizes. The unpublished manuscript PowerLawModelsMethodsREV1 reviews current stochastic models and presents a wavelet-based analysis procedure for identifying data segments that can be characterized by a generalized power-law structure model. A classifier finds a two-component power-law fit with a goodness-0f-fit measure using wavelet scale spectra.
As discussed in detail, wavelet scale spectra are particularly well suited for analyzing the class of non-stationary fractional Brownian motion (fBm) processes introduced by Benoit Mandlebrot. FBm processes have a self-scaling property akin to fractals that is often invoked to characterize the structure cascade associated with convective instabilities. The paper establishes a framework for data analysis and, ultimately, structure model improvement. This material updates and replaces earlier blogs that addressed the same material.