Probability distributions of bed load particle velocities, accelerations, hop distances, and travel times informed by Jaynes's principle of maximum entropy. Issue 7 (27th July 2016)

• Record Type: Journal Article
• Authors: Furbish, David Jon; Schmeeckle, Mark W.; Schumer, Rina; Fathel, Siobhan L.
• Is Part Of: Journal of geophysical research. Volume 121:Issue 7(2016)
• Page Start: 1373
• Page End: 1390
• Publication Date: 2016-07-27
• Subjects: bed load sediment -- maximum entropy -- probability distribution; Geomorphology -- Periodicals; 551.3
• DOI: 10.1002/2016JF003833
• Languages: English
• ISSNs: 2169-9003

Abstract

Abstract: We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high‐resolution measurements obtained from high‐speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight. Key Points: The maximum entropy method is equally grounded in statistical mechanics and inferential statistics The method honors mechanical constraints imposed by equilibrium transport conditions The distributions are consistent with high‐resolution imaging of bed load particle motions