Simplified models that capture the essential elements of physical phenomena are used extensively. The equivalent phase-screen model is a case in point, but the approximation is not overly constraining. As as long as the structure encountered is statistically uniform or slowly varying along the propagation path, scintillation well removed from the structured region is statistically indistinguishable from a full-diffraction simulation. However, two-dimensional propagation is fundamentally different from three-dimensional propagation. For example, phase screens with no variation along one direction launch cylindrical waves, which vary as 1/r.

A compelling reason for using two-dimensional models is that diagnostic measurements are time series. As shown in the book Chapter 4, an effective scan velocity converts the time to spatial distance within a two-dimensional field. Propagation from a one-dimensional phase screen generates a one-dimensional field that can be compared directly to a diagnostic data. The two-dimensional phase-screen theory provides a complete model of one-dimensional scintillation from a phase-screen with prescribed power-law parameters. Moreover, there is a closed-form solution for the intensity spectral density function SDF.

With a combination of asymptotic approximations and numerical integration, Charlie Carrano developed a very efficient calculation of the intensity SDF REF In the reference he also demonstrated an irregularity parameter estimation (IPE) scheme to find the parameters that provided a *best match* to a measured SDF. The initial goodness of fit measure was the least squares error of the logarithms of the measured and theoretical SDFs. A more refined Maximum Likelihood goodness-of-fit measure was later introduced REF.

To the extent that IPE generates parameters that match real data, a phase-screen model can be used to generate frequency-dependent scintillation realizations for system analysis. The paper “A compact multi-frequency GNSS scintillation model,” published in the Institute of Navigation Journal describes such a model for GPS scintillation. Cited references demonstrate validation. A MatLab implementation of the model can be down loaded from github.com.

## About Chuck

Retired research engineer. Recently published book "The Theory of Scintillation with Applications in Remote Sensing," John Wiley IEEE Press, 201