Stochastic variability of fluvial hydraulic geometry: Mississippi and red rivers

Major reasons for uncertainty in engineering predictions of river flows are the spatial variability and measurement error associated with depicting channel geometry. This paper develops a descriptive spatial stochastic model of depth-based hydraulic geometry in application to four dense data sets from the Mississippi and Red Rivers. To represent the irregularity in flow area and hydraulic radius as functions of flow depth, at-a-station cross-section geometry is defined using regressed power functions, accompanied by random residuals. More than 1600 surveyed cross sections are analyzed to describe trends in the spatial variance, and gradual (large-scale) and periodic (medium-scale) trends in the spatial mean of cross-sectional geometry parameters and channel bed slope. Also described are the probability distribution and correlation structure of each parameter's random component. The relationships between spatial statistics of hydraulic geometry and bankfull width, channel sinuosity (meander patterns), bed elevation and riffle-pool spacing, and bank composition are explored. Conclusions and implications are discussed regarding the variable nature of fluvial hydraulic geometry and regarding the incorporation of geometric parameter uncertainty into prescriptive models of river processes.