Statistical models of fluvial systems

Statistical methods have dominated quantitative analyses of fluvial systems over the last 40 years. This paper assesses the utility of statistical models by examining methodological issues associated with empirical analysis of hydraulic and channel geometry relationships. It also describes and presents examples of advanced statistical models that promise to enhance our understanding of the structure and dynamics of fluvial systems. Bivariate and multivariate power function models of fluvial systems provide objective numerical descriptions of the relationship between channel geometry and hydrologic, hydraulic, sedimentologic, and biotic controls. Traditional regression models are limited in that they only describe simple input-output relations between the states of dependent and independent variables. Advanced statistical models transcend these limitations. Simultaneous-equation models, continuously-varying parameter models, and distributed lag models are statistical tools for explicitly analyzing: (1) mutual adjustments among fluvial variables, (2) the factors controlling the spatial structure of channel geometry-flow relations, and (3) the equilibrium or disequilibrium dynamics of fluvial systems, respectively. These advanced statistical techniques can be used to empirically test conceptual models of fluvial systems at a variety of spatial and temporal scales.