Logratio linear modelling of hydraulic geometry using indices of flow resistance as covariates

Abstract

The exponents of hydraulic geometry relations are unit-sum constrained (i.e., a composition), thus, a class of statistical methods called compositional data analysis must be employed to obviate the problem of spurious correlation. One of these methods, logratio linear modelling, is capable of establishing either linear or non-linear functional dependency between a composition (e.g., hydraulic geometry exponents) and a covariate. In our study, logratio linear modelling of data from the literature did not establish correlations between at-a-station hydraulic geometry and median grain size (d 50) of the bed material, stream roughness, nor drag resistance. The lack of a correlation between at-a-station hydraulic geometry and bed grain size is expected in streams where roughness is dominated by planform characteristics, vegetation elements, macroscale bar features, channel obstructions, or bedforms. The use of d 84 in the Prandtl-von Karman “law of the wall” equation and in the Keulegan resistance equation, however, suggests that d 84 might have been a more appropriate parameter to use than d 50. The lack of a correlation between at-a-station hydraulic geometry and stream roughness (or drag resistance) is expected in streams where roughness elements become rapidly “drowned” at higher discharges. Hydraulic geometry, however, was shown to be a function of the rate at which stream roughness varies with discharge. Thus, to understand the complex interactions within fluvial systems, geomorphologists should examine the rates of change of stream parameters such as drag resistance, Manning's roughness coefficient, the Darcy-Weisbach friction factor, and grain size indices, in addition to the stream parameters themselves.