The blog on irregularity parameter estimation (IPE) introduced a paper that used realizations of a stochastic processes with a prescribed spectral density function (SDF). Such realizations are generated by imposing the square root of the desired SDF on a collection of zero-mean, unit-variance, uncorrelated Fourier modes. Consequently, the realizations are zero-mean and symmetric statistically. Real-world applications generate SDFs from measurements of non-negative statistically asymmetric ionospheric electron density structure or diagnostic electromagnetic wave intensity scintillation measurements.
An SDF is formally the average intensity of spatial Fourier transformations of process realizations. The configuration features that distinguish different underlying physical structure defined by the discarded Fourier-domain phase structure. The discarded phase structure structure contains the information that distinguishes different physical processes. A complete statistical description would include a probability density function and higher-order correlations.
The blog on irregularity parameter estimation also included a report showing that IPE applied scintillation intensity realizations derived from random phase screens recovers the input phase-screen parameters. The blog Equatorial Plasma Bubbles reviewed IPE estimates of power-law parameters from physics-based realizations of intense ionospheric structure. The statistical similarity of diverse processes with the same SDF is well established. Even so, it is desirable to generate realizations that are closer to the physical structure of the underlying process.
As an alternative to building structure realizations from amplitude weighted random Fourier modes, configuration-space models use random collections of striations. A striation is an ionization distribution tied to individual field lines, basically a radial distribution of ionization with a characteristic strength and scale. The link shows a dramatic visualization of collections of striations that comprise equatorial ionospheric disturbances.
In the recently submitted paper A Configuration Space Model for Intermediate-Scale Ionospheric Structure, we show that three-dimensional realizations of striations can be generated with size and strength distributions that support a prescribed SDF. The left frame in the figure below from the paper shows a cross-field slice of a three-dimensional realization. The right frame shows the target theoretical, the expectation theoretical, and measured average one-dimensional SDFs.