Reenvisioning cross-sectional at-a-station hydraulic geometry as spatially explicit hydraulic topography

- Classical hydraulic geometry depends on unrealistic assumptions and unavoidable sampling bias.
- We developed a new method to assess discharge-dependent hydraulics called hydraulic topography.
- Width, depth, and velocity were analyzed and compared at three spatial scales.
- Results show that hydraulic geometry is less accurate and less representative than believed.

Transect-based hydraulic geometry is well established but depends on a complex set of subjective fieldwork and computational decisions that sometimes go unexplained. As a result, it is ripe for reenvisioning in the light of the emergence of meter-scale, spatially explicit data and algorithmic geospatial analysis. This study developed and evaluated a new spatially explicit method for analyzing discharge-dependent hydraulics coined 'hydraulic topography' that not only increases accuracy but also eliminates several sample- and assumption-based inconsistencies. Using data and hydrodynamic simulations from the regulated, gravel-cobble-bed lower Yuba River in California, power functions were fitted to discharge-dependent average width, depth, and depth-weighted velocity for three spatial scales and then their corresponding exponents and coefficients were compared across scales and against ones computed using traditional approaches. Average hydraulic values from cross sections at the segment scale spanned up to 1.5 orders of magnitude for a given discharge. Transect-determined exponents for reach-scale depth and velocity relations were consistently over- and underestimated, respectively, relative to the hydraulic topography benchmark. Overall, 73% of cross-sectional power regression parameters assessed fell between 10 and 50 absolute percent error with respect to the spatially explicit hydraulic topography baseline. Although traditional transect-based sampling may be viable for certain uses, percent errors of this magnitude could compromise engineering applications in river management and training works.