Glacier Flow Simulator: Ice Deformation & Glen's Flow Law

simulator intermediate ~10 min
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u_s = 42 m/yr — moderate valley glacier flow

A 500 m thick glacier on a 5° slope at -10°C flows at approximately 42 m/yr at the surface, with internal deformation accounting for most of the motion and basal sliding contributing additional velocity.

Formula

u_s = (2A/(n+1)) × (ρg sinα)^n × H^{n+1}, n = 3
τ_b = ρgH sinα (basal shear stress)
A(T) = A_0 × exp(-Q/(RT)) (Arrhenius temperature dependence)

Rivers of Ice

Glaciers are rivers of ice that flow under their own weight. Unlike water rivers driven by pressure gradients, glacier flow is a slow-motion creep driven by gravity acting on enormous ice masses. A typical valley glacier moves meters per year — imperceptibly slow to the eye, but over centuries it carves U-shaped valleys, deposits moraines, and reshapes entire landscapes. Understanding glacier flow is essential for predicting how ice sheets will respond to climate warming.

Glen's Flow Law

Ice deforms as a non-Newtonian fluid described by Glen's flow law: the strain rate is proportional to the shear stress raised to the power n≈3. This nonlinearity has profound consequences — doubling the stress increases flow rate eightfold. The rate parameter A depends exponentially on temperature through the Arrhenius equation, making warm ice near the melting point flow roughly 1,000 times faster than ice at -40°C. This simulation lets you explore how thickness, slope, and temperature interact to determine glacier velocity.

Basal Sliding and Water

Beneath many glaciers lies a thin layer of water at the pressure melting point. This water lubricates the bed, allowing basal sliding that can exceed internal deformation as the dominant flow mechanism. Subglacial water pressure is the key control: when water pressure approaches ice overburden pressure, the effective friction drops dramatically. Seasonal meltwater pulses reaching the bed through moulins explain why glaciers accelerate in summer — and why increasing surface melt under climate change may destabilize ice sheets.

Ice Streams and Fast Flow

Ice streams are corridors of fast-flowing ice within ice sheets, moving 100–1,000 m/year compared to surrounding ice at 1–10 m/year. They drain the majority of ice from Antarctica and Greenland. Their speed is controlled primarily by basal conditions: soft, water-saturated sediment beneath allows rapid sliding. Ice stream dynamics are the largest source of uncertainty in sea level rise projections because their behavior can change abruptly and is difficult to model accurately.

FAQ

How do glaciers flow?

Glaciers flow through two mechanisms: internal deformation (ice crystals slowly creep under their own weight via dislocation glide) and basal sliding (the glacier slides over its bed on a thin water film). Internal deformation follows Glen's flow law, where strain rate is proportional to stress raised to the power n≈3. Warm, thick glaciers on steep slopes flow fastest.

What is Glen's flow law?

Glen's flow law relates strain rate to stress in ice: ε̇ = Aτ^n, where A is a temperature-dependent rate factor and n≈3. This nonlinear rheology means doubling the stress increases the flow rate eightfold. It was established experimentally by John Glen in the 1950s and remains the foundation of glacier dynamics modeling.

How fast do glaciers move?

Typical valley glaciers move 10-200 m/year. Ice streams in Antarctica can reach 1 km/year. Jakobshavn Glacier in Greenland, one of the fastest, moves over 40 m/day. Glacial surges can temporarily increase speeds tenfold. The variation depends on ice thickness, slope, temperature, and basal conditions.

What is basal sliding?

Basal sliding occurs when the glacier base reaches the pressure melting point and a thin water layer forms between ice and bedrock. The sliding velocity depends on basal shear stress and effective pressure (ice overburden minus water pressure). High water pressure dramatically reduces friction, explaining seasonal speed-ups when meltwater reaches the bed.

Sources

Embed

<iframe src="https://homo-deus.com/lab/glaciology/glacier-flow/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub