METHODOLOGY: DISCRIMINANT FUNCTION ANALYSIS OF COMPOSITIONAL DATA: AN EXAMPLE FROM HYDRAULIC GEOMETRY

Many of the data sets analyzed by physical geographers are compositional in nature: they have row vectors that add to one (or 100%). These unit-sum constrained data sets should not be analyzed by standard multivariate statistical methods. Significant differences were found in the log-ratio mean vectors of the hydraulic exponents (which are unit-sum constrained) for two classes of streams: those with cohesive, non-vertical banks, and those with one firm and one loose bank. Compositional discriminant function analysis of bank stability on the basis of hydraulic geometry had a success rate of 88%, making routinely archived measurements of stream width, cross-sectional area, mean velocity, and discharge a readily available data base for predicting the stability of stream reaches. Key words: geomorphology, hydraulic geometry, discriminant function, statistics.]