(0.92 – 1.80 ft)

(1.08 – 2.00 ft)

(1.44 – 2.40 ft)

Meltwater flows on the surface of and with glaciers and other ice sheets are important relative to the addition of liquid water into Earth’s oceans, and to bulk motions of the glaciers and ice sheets. Glacial meltwater might flow along the surface like a stream or river, accumulate in surface lakes, flow downward into open crevasses or moulins, accumulate as lakes interior to the ice mass, flow as a sheet of liquid between the ice bottom and bedrock, or flow enclosed in channels partially or completely embedded within the ice mass.

Flows that reach the boundary of the ice sheet deplete the ice mass balance and can contribute to sea level rise if the flow reaches the sea.  Meltwater remaining on the surface of the glacier or ice sheet can refreeze and have no impact on the glacier mass balance.  Flows reaching the base of the glaciers by way of crevasse and moulins are considered to provide potential lubrication and flotation that enhances bulk ice motions.

How solid is the foundation for simulating glacial meltwater flows that are included in projections of ice sheet melting?

Glacial meltwater flows have been modeled for more than four decades using thermal-hydraulic modeling.  The widely used Springer-Hutton formulation is based on principles of continuum mechanics, and detailed mathematical reduction to the standard 1-dimensional channel- average form for engineering applications. A steady-state energy balance equation is applied to flow of liquid water in ice channels embedded in large ice masses. The Spring-Hutter system considers the case of evolution in time and space of the flow area of the channel. Changes in flow area are caused by ice melting and dynamics of the ice in which channels are located. There have been numerous studies providing clarifications, modifications and applications of Spring-Sutter framework.

New paper

I have conducted a detailed analysis of the Spring-Sutter equations and their solutions in this paper [EDHmelt]

The paper clarifies and improves calculations of the role of viscous dissipation of kinetic energy into thermal energy as this physical process appears in models of meltwater flows embedded in and at the boundaries of glaciers and ice sheets.

Meltwater flows on the surface of and within glaciers and other ice sheets are important relative to the addition of liquid water into Earth’s oceans, and to bulk motions of the glaciers and ice sheets. Glacial meltwater might flow along the surface like a stream or river, accumulate in surface lakes, flow downward into open crevasses or moulins, accumulate as lakes interior to the ice mass, flow as a sheet of liquid between the ice bottom and bedrock, or flow enclosed in channels partially or completely embedded within the ice mass.

Flows that reach the boundary of the ice sheet deplete the ice mass balance and can contribute to sea level rise if the flow reaches the sea.  Meltwater remaining on the surface of the glacier or ice sheet can refreeze and have no impact on the glacier mass balance.  Flows reaching the base of the glaciers by way of crevasse and moulins are considered to provide potential lubrication and flotation that enhances bulk ice motions.

A dimensionless form for steady-state energy balance for the liquid, accounting for effects of meltwater on the bulk liquid, is developed and solved. Analytical solutions of the temperature distribution along the channel are developed. The solutions explicitly illustrate effects of viscous dissipation of kinetic energy into heat, and the consequence effects on melting ice at the liquid-ice interface.

The paper shows that:

• Letting viscous dissipation of kinetic energy go directly into melting is not correct
• The energy equations are not complete because they do not account for meltwater entering the bulk liquid
• The Spring-Hutter accounting for meltwater entering the bulk liquid is not correct.