Modeling the general pdf of intensity in terms of the scattering parameters for WPRM

The intensity correlations for WPRM can be predicted for forward scatter from solutions of the parabolic 4th moment when the space‐time autocorrelation function, the scattering stength parameter γ, and the scaled range X are known. Thus, the intensity variance and its time/depth correlations can be predicted. However, the intensity pdf has not been predicted for all ranges of γ and X. T. Ewart and D. Percival [J. Acoust. Soc. Am. 80, 1745–1753 (1986) I have shown that the generalized gamma distribution function (GGDF) models the probability distribution of intensity in forward scattering over wide ranges in γ and X. In this study the two parameters of the GGDF are obtained as functions of γ and X by fitting the distribution to many realizations of simulated intensity data. Realizations of the intensity were generated by Monte‐Carlo techniques [C. Macaskill and T. Ewart, IMA J. Appl. Math. 33, 1–15 (1984)]. The mapping of the distribution parameters to γ and X provides a convenient way to examine the behavior of the distributions as they vary smoothly from lognormal to exponential with increasing X for constant values of γ. A heuristic model of the mapping is presented. Implications and future expectations are discussed. [Work supported by ONR.]