Composite roughness of rectangular ice-covered rivers

Composite roughness is a crucial parameter in determining the stage-discharge relationship using Manning's formula. Due to the increased resistance resulting from ice cover, a stage-discharge relationship developed in open water is not applicable to the ice-affected reason. This calls for the development of a new stage-discharge relationship. According to the Einstein hydraulic radius separation theory, the flow cross section of a rectangular ice-covered river may be divided into bed, ice and side-wall subsections. Based on the determination of hydraulic radius and sectional area of each flow subsection, this paper presents an analytical solution of composite roughness for flows in rectangular ice-covered rivers. Comparisons of the calculated results with measured data from literature show that the proposed formula does well in predicting the composite roughness of rectangular ice-covered rivers. Compared with Einstein formula and Sabaneev formula, the proposed formula produces more accurate results. For wide ice-covered rivers, if width-depth ratio is greater than 20, hydraulic radius may be considered approximately equivalent to flow depth as a simplification of relatively high precision.