Previous blogs have outlined the development of irregularity parameter estimation (IPE) as applied to ionospheric scintillation data and to simulations as described in Rino and Carrano and Rino, Carrano, and Yokoyama, respectively. The applications of IPE assume diagnostic measurements are characterized by two-component power-law SDFs. The theory of stochastic processes provides a framework for generating abstract realizations of processes that have statistically similar coherence properties. However, the physical phenomenon of interest is the evolving three-dimensional ionospheric irregularity structure, particularly equatorial spread F which refers to diagnostic HF sounder back scatter from equatorial plasma bubbles (EPBs).

Whereas the structure that immediately identifies EPBs depends on configuration, SDFs ignore the phase of the Fourier components that define the structure. Furthermore, Fourier components that equate wavelength and structure scale are not physically realizable. Configuration-space models use random configurations of three-dimensional physically realizations of striations with definitive scales as described in Rino and Carrano. The fact that the configuration space-model provides both physical realizations and SDFs makes it ideally suited for validating propagation models, which start with three-dimensional structure models an predict diagnostic measurements. Of particular interest are two-dimensional propagation models and the equivalent phase-screen model. The interrelations are developed in Rino and Carrano.

Most recently we have begun to consider some broader issues regarding structure models. Ionospheric physics is concerned with all aspects of the earth’s ionosphere, which are generally manifest in changes of the electron density as a function of position and time. Ionospheric models capture the attributes that can be represented with parameterized mathematical expressions. These quasi-equilibrium models provide starting point for incorporating ionospheric disturbances, which may themselves admit analytic characterization. Internal waves provide an example. Stochastic structure does not admit direct mathematical realization except through physics-based simulations. Furthermore, there is no definitive scale at which structure transitions from quasi-deterministic to stochastic. In a diagnostic measurement segments that support stochastic characterization must be identified. More formally, the density structure must be broken down by scale. At some point in this process the sub structure is effectively stochastic and locally in-homogeneous.

An approach to ionospheric modeling and segmentation was introduced at a Living With a Star workshop presentation. A detailed discussion can be found in an unpublished note. With the global ionospheric coverage provided through the GNSS satellites, direct measurement of total electron content (TEC) is particularly appealing. In particular, the gigahertz frequencies used by the GNSS satellites is by design minimally affected by scintillation. By design GNSS satellites are minimally affected by propagation disturbances, whereby global TEC observations can be processed to extract stochastic structure, as described in Rino et al.