The discharge of natural rivers is one of the important hydrological factors that are considered when responding to ice-flood disasters during ice periods. Traditionally, holes need to be dug along the cross-section on the ice cover to gauge velocity distributions along the flow depth at each hole, and to calculate the cross-sectional flow discharge by integrating velocity profiles over the entire area. This method is time consuming, costly, and inefficient. The discharge measurement can be improved using the sectional flow-depth distribution and stream-tube methods. However, the selection of both the depth-averaged–velocity-estimation method and the typical survey-point position in the cross-section affects the estimation accuracy. This study first compared the estimation methods of the depth-averaged velocity, such as the one-, two-, three-, and six-point methods, and their estimation accuracy. Furthermore, the variations in relative-unit discharge distributions in common channels with cross-sectional topographies were analyzed, and the effects of the cross-section characteristic coefficient and typical survey-point position on the flow-discharge estimation accuracy were compared. The results show that the average errors of the depth-averaged velocity estimated by the one-point method at 0.5H, new three-point method, and six-point method were 1.96%, 1.22%, and 0.45%, respectively. The new three-point method is recommended if measurement workload and accuracy are key considerations. The cross-section characteristic coefficient is considered to be 0.5 and 0.25 for the natural river and artificial channel, respectively, and the maximum-flow-depth position in the mainstream area of the cross-section is selected as the typical survey-point position. Thus, the flow-discharge estimation accuracy can be improved. In conclusion, this study provides an improved stream-tube method for the measurement of flow discharge and velocity distribution in ice periods, which can be used as a reference during practical applications.

Various empirical equations for mean bed and wall shear stresses have been proposed for smooth rectangular open channels. Considering that the distribution of bed shear and wall shear stresses is affected by the cross-sectional shape, the gravity force based on the flow depth used to non-dimensionalize shear stresses in previous studies is modified to a parameter that includes the width and wetted-perimeter. This yields a new set of dimensionless equations for mean bed and wall shear stresses, and the wall/bed shear force ratio. These equations compared well with all available experimental data over a wide range of aspect ratios from 0.31 to 50. These equations also yield new relationships for bed and wall friction factors.

A two-dimensional wave model coupled with ice dynamics is developed to evaluate ice effects on shallow water wave propagation on a beach and in a channel. The nonlinear Boussinesq equations with ice effects are derived and solved by the hybrid technique of the Godunov-type finite volume method and finite difference method with the third-order Runge–Kutta method for time integration. The shock capturing method enables the model to simulate complex flows over irregular topography. The model is capable of simulating wave propagations accurately, including non-hydrostatic water pressure and wave dispersions. The ice dynamic module utilizes a Lagrangian discrete parcel method, based on smoothed particle hydrodynamics. The Boussinesq wave model is validated with an analytical solution of water surface oscillation in a parabolic container, an analytical solitary wave propagation in a flat channel, and experimental data on tsunami wave propagations. The validated model is then applied to investigate the interaction between ice and tsunami wave propagation, in terms of ice attenuation on tsunami wave propagations over a beach, ice deposition on the beach driven by the tsunami wave, and ice jam formation and release in a coastal channel with the intrusion of the tsunami wave. The simulated results demonstrated the interactions between tsunami waves and surface ice, including the maximum run up, ice movement along the beach, and ice jamming in a channel.

Traditional discharge measurements in ice‐covered river channels are time‐consuming and costly, thus limiting the elucidation of flow patterns during winter. This study proposes an analytical model for quantifying the transverse distributions of the unit‐width discharge and the depth‐averaged streamwise velocity in ice‐covered channels by extending an existing stream‐tube method to include the effects of cover and bed roughness and cross‐sectional geometry. A new set of equations are obtained for this extended method. An empirical coefficient α is included to lump the effects of the shape and friction factors of the ice cover and the channel bed. The model is compared with flume experiments and field data for fully and partially ice‐covered flows to examine the variation of the coefficient α.