Formulating flows in frozen rivers

As the northern hemisphere approaches another potentially more extreme winter, many normally free-flowing rivers are at greater risk of freezing over.

The latest issue (165 WM9) of the ICE Water Management journal looks at the increasing importance to civil engineers of knowing how this will affect water yields and sedimentation, given society’s dependence on rivers for water supply.

Understanding the flow

Normally a river’s flow rate can be estimated from the Manning formula, which is based on the cross-section and slope of the channel and the roughness of the river bed. But when frozen over, the water is additionally slowed by the underside of the ice.

This requires a ‘composite’ Manning’s coefficient to be estimated, representing the roughness of the bed and ice together.

In his paper, Samuel Li of Concordia University in Canada says management of seasonally ice-covered rivers is critical to planning, design and operation of water resources projects. "To address these issues properly entails a good understanding of the hydraulics of ice-covered rivers, where the composite Manning’s coefficient is fundamental."

Overcoming these challenges

Using extensive flow data from 13 seasonally frozen rivers in Canada, which were blanketed in up to one metre of ice, Li has found a remarkably consistent method of estimating the combined roughness coefficient of an iced over channel.

"The results show that the composite Manning coefficient ranges from 0.013 to 0.040 as winter averages, but can vary up to seven-fold through the winter," he concludes.

The estimates reported in the paper will be useful to all civil engineers needing to model the effects of ice cover on river discharges and sedimentation.

For more information please contact the ICE Proceedings editor Simon Fullalove on +44 20 7665 2448, or at