Order parameter for morphodynamic transitions in braided rivers: A stochastic compositional framework.

We develop a stochastic simplex framework for width partitioning in braided river cross sections, modeling normalized channel widths as random compositional vectors. Two complementary models are introduced: the symmetric Dirichlet distribution, which models width allocation as exchangeable stochastic fluctuations around a uniform baseline with no preferred channel, and the isotropic logistic-normal distribution, which accommodates systematic width concentration through a single scale parameter. Both models carry independent physical content: the Dirichlet characterizes morphodynamic states in which all channels are statistically equivalent, while the logistic-normal identifies and quantifies organized concentration regimes. We derive exact closed-form expressions for the expected concentration index and width concentration fraction under both models, establish a parameter-free structural breakdown criterion, and analyze the temporal evolution of model parameters across 11 annual surveys of the Brahmaputra-Jamuna River (Bangladesh) spanning 1976-2007. The analysis reveals a decadal-scale morphodynamic transition: for 1976-1985, width is distributed among channels in a statistically uniform fashion consistent with the Dirichlet model. From 1995 onwards, a progressive increase in the logistic-normal scale parameter σ^{*}, optimized independently for each survey year and fitted by a logistic regression (R^{2}=0.997), indicates systematic growth of channel width concentration. A parameter-free structural breakdown criterion certifies the failure of the Dirichlet model between 1995 and 1999, where the logistic-normal model recovers goodness-of-fit values above 0.95. Both σ^{*} and the Dirichlet parameter c^{*} retain memory of the concentration phase above pretransition levels throughout the observational window.