From Climate etc.
by Dan Hughes
This post challenges conventional frameworks for simulating meltwater flow in glaciers and ice sheets.
Increased melting rates due to potential increases in temperature will increase liquid water directly into the ocean. An additional aspect is that the melt water, when it reaches the base of the glacier, can cause the glacier to rise and cause calving at the terminal.
The World Resources Institute (WRI) has summarized the results of the IPCC AR6 on the melting of the Greenland and Antarctic ice sheets:
If warming reaches between 2 degrees C (3.6 degrees F) and 3 degrees C (5.4 degrees F), for example, the West Antarctic and Greenland ice sheets could melt almost completely and irreversibly for thousands of years, causing sea ​​level rises. a few meters.
| Increase Temperature | 1.5 C (2.7 F) | 2.0 C (3.6 F) | 3.0 C (5.4 F) |
| Average global sea level will rise by 2100 | 0.28 – 0.55 m(0.92 – 1.80 ft) | 0.33 – 0.61 m(1.08 – 2.00 ft) | 0.44 – 0.76 m(1.44 – 2.40 feet) |
Meltwater flows on the surface and with glaciers and other ice sheets are important relative to the addition of liquid water to the Earth’s oceans, and the movement of many glaciers and ice sheets. Glacial meltwater can flow along the surface as a river or stream, collect in surface lakes, flow down into crevasses or open moulins, collect as lakes within ice masses, flow as liquid sheets between the ice base and bedrock, or flow . attached to the channel partially or completely attached to the mass of ice.
Flow reaching the ice sheet boundary reduces the ice mass balance and can contribute to sea level rise if the flow reaches the ocean. The remaining melt on the surface of the glacier or ice sheet can refreeze and have no effect on the mass balance of the glacier. Streams that reach the base of the glacier by way of crevasse and moulin are thought to provide lubrication and flotation potential that promotes bulk ice movement.
How solid is the basis for simulating glacial meltwater flows included in ice melt projections?
Glacial meltwater flow has been modeled for more than four decades using thermal-hydraulic models. The widely used Springer-Hutton formulation is based on the principles of continuum mechanics, and a detailed mathematical reduction to a standard 1-dimensional channel mean form for engineering applications. The steady-state energy balance equation is applied to the flow of liquid water in an ice channel embedded in a large ice mass. The Spring-Hutter system considers the case of evolution in time and space of the flow area of ​​the channel. Changes in the flow area are caused by the melting of the ice and the dynamics of the ice where the channel is located. There are many studies that provide clarification, modification and application of the Spring-Sutter framework.
New paper
I have conducted a detailed analysis of the Spring-Sutter equation and its solution in this paper (EDHmelt)
The paper clarifies and improves the calculation of the role of kinetic energy dissipation into thermal energy as this physical process is seen in models of meltwater flow embedded in and at the boundaries of glaciers and ice sheets.
Meltwater flows on the surface and in glaciers and other ice sheets are important relative to the addition of liquid water to the Earth’s oceans, and the movement of many glaciers and ice sheets. Glacial meltwater can flow along the surface as a river or stream, collect in surface lakes, flow down into crevasses or open moulins, collect as lakes within ice masses, flow as a liquid sheet between the ice base and bedrock, or flow . attached to the channel partially or completely attached to the mass of ice.
Flow reaching the ice sheet boundary reduces the ice mass balance and can contribute to sea level rise if the flow reaches the ocean. The remaining melt on the surface of the glacier or ice sheet can refreeze and have no effect on the mass balance of the glacier. Streams that reach the base of the glacier by way of crevasse and moulin are thought to provide lubrication and flotation potential that promotes bulk ice movement.
A dimensionless form for the steady-state energy balance for fluids, accounting for the effect of melting water on bulk fluids, is developed and solved. An analytical solution of the temperature distribution along the channel is developed. The solution clearly illustrates the effect of viscous kinetic energy dissipation to heating, and the consequent effect on ice melting at the liquid–ice interface.
The paper shows that:
- Allowing the viscous kinetic energy to dissipate directly into the melt is incorrect
- The energy equation is incomplete because it does not account for meltwater entering the bulk liquid
- Spring-Hutter’s accounting for meltwater entering the bulk liquid is incorrect.
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