Research papersIntegrating hydraulic equivalent sections into a hydraulic geometry study

•The stage Z-discharge Q relationship in GVFAR was derived.•The AHG of alluvial channels in the Songhua and the Yangtze River was obtained.•The concept of hydraulic equivalent section was presented.•The cross section of GVFAR was generalized into hydraulic equivalent section.•Bed-building properties between GVFAR and equivalent section were compared.

Hydraulic geometry (HG) is an important geomorphic concept that has played an indispensable role in hydrological analyses, physical studies of streams, ecosystem and aquatic habitat studies, and sedimentology research. More than 60 years after Leopold and Maddock (1953) first introduced the concept of HG, researchers have still not uncovered the physical principles underlying HG behavior. One impediment is the complexity of the natural river cross section. The current study presents a new way to simplify the cross section, namely, the hydraulic equivalent section, which is generalized from the cross section in the “gradually varied flow of an alluvial river” (GVFAR) and features hydrodynamic properties and bed-building laws similar to those of the GVFAR. Energy balance was used to derive the stage Z-discharge Q relationship in the GVFAR. The GVFAR in the Songhua River and the Yangtze River were selected as examples. The data, including measured discharge, river width, water stage, water depth, wet area, and cross section, were collected from the hydrological yearbooks of typical hydrological stations on the Songhua River and the Yangtze River from 1955 to 1987. The relationships between stage Z-discharge Q and cross-sectional area A-stage Z at various stations were analyzed, and “at-a-station hydraulic geometry” (AHG) relationships were obtained in power-law forms. Based on derived results and observational data analysis, the Z-Q and Z-A relationships of AHG were similar to rectangular weir flows, thus the cross section of the GVFAR was generalized as a compound rectangular, hydraulic equivalent cross section. As to bed-building characteristics, the bankfull discharge method and the stage-discharge-relation method were used to calculate the dominant variables of the alluvial river. This hydraulic equivalent section has the same Z-Q relation, Z-A relation, dominant discharge, dominant river width, and dominant water depth as the cross section in the GVFAR. With the hydraulic equivalent section, the relationships between the discharge and river width, river depth, and width-to-depth ratio are easier to depict in DHG analysis. Replacement of the cross section in the GVFAR with the hydraulic equivalent section is expected to promote further development of HG.