Comparative hydraulic geometry using compositional data analysis and stochastic modelling

Exponents of hydraulic geometry relationships are unit-sum constrained, which requires that they be analyzed by statistical methods designed for compositional data. Because the derivatives at a given discharge of log-quadratic relationships are unit-sum constrained, non-linear systems can also be studied by compositional methods.; Analysis of data from the literature revealed significant differences in the logratio means and covariances of the hydraulic geometry of various categories of streams within a given climate, but not always between climates, indicating that local factors have more influence on hydraulic geometry than does climatic setting. Discriminant function analysis of bank stability on the basis of hydraulic geometry had a success rate of 88 percent, making routinely archived measurements of stream width, area, velocity, and discharge an effective data base for a regional search for streams with stable banks.; Logratio linear modelling of hydraulic geometry determined for nine cross-sections in the Sabine River Basin and of data from the literature failed to establish significant correlations between hydraulic geometry and median size of the bed material, stream roughness, slope, and drainage area. Hydraulic geometry did correlate with the rates at which stream roughness and friction factor vary with discharge.; Logcontrast principal components analysis revealed that ninety-seven percent of the total variation of the at-a-station hydraulic geometry for the Sabine River Basin stations in Texas can be accounted for by the first logcontrast principal component. Compositional hypothesis tests of comparisons of computer-generated distributions of hydraulic exponents with natural and flume study distributions showed that a model based on minimum variance theory that involves optimization of a function with two random variables and a model based on stochastic perturbation of a composition both provide realistic simulations of the distributions of naturally occurring hydraulic exponents.