This simulation models an alpine valley glacier flowing down a linear bedrock slope using the shallow-ice approximation of Glen's flow law. Ice thickness on a 200-cell, 6 km grid evolves by mass-conservation continuity: the depth-integrated flux follows Q = (2A/(n+2))(ρg sinα)nHn+2, with flow-rate factor A = 2.4×10-24 Pa-3s-1, exponent n = 3, ice density ρ = 917 kg/m³.
The sliders set a temperature anomaly (−4 to +6 °C), snowfall rate (0.2–3.0 m/yr), bed slope (4–30°) and simulation speed (1–20×). Surface mass balance is positive above the Equilibrium Line Altitude and negative below it, and warming raises the ELA by 150 m per °C. The model shows why real glaciers advance, retreat and leave moraines as climate shifts.
What does this simulation show?
It shows a cross-section of an alpine valley glacier flowing downhill and responding to climate. You watch the ice advance or retreat, see faster flow tinted orange, the Equilibrium Line Altitude marked by a yellow dashed line, and brown moraine left behind at the glacier's furthest past extent.
What is Glen's flow law?
Glen's flow law describes how glacier ice deforms as a non-linear viscous fluid: strain rate is proportional to stress raised to the power n (here n = 3). The simulation uses it to compute the depth-integrated ice flux, so thick, steep ice flows far faster than thin or gently sloping ice.
What is the ELA and why does it matter?
The Equilibrium Line Altitude is the elevation where annual accumulation exactly balances annual melt. Above it the glacier gains mass; below it it loses mass. The model starts the ELA at 2200 m and raises it 150 m for every +1 °C, so a warmer climate shrinks the accumulation zone and starves the glacier.
Temperature anomaly shifts the ELA up or down; snowfall rate caps how much ice can accumulate per year; slope angle rebuilds the bedrock and changes the driving stress and flow speed; and simulation speed runs more physics steps per frame so you reach long-term equilibrium faster.
Velocity is estimated from the deformation term of Glen's law, roughly v ∝ A(ρg sinα)nHn, where H is local ice thickness and α is the bed slope. The faster-flowing cells are shaded orange in the cross-section, and the maximum speed in metres per year is shown in the statistics panel.
It captures the correct qualitative physics and uses realistic constants, but it is deliberately simplified. It is one-dimensional, ignores basal sliding, longitudinal stress coupling, valley-width variation and ice temperature, and the time-stepping is a teaching scheme. Trends are meaningful; precise numbers are illustrative rather than predictive.
The model records the greatest ice thickness ever reached in each grid cell. When the glacier later thins or retreats from that position, the difference is drawn as brown sediment, mimicking lateral and terminal moraines that real glaciers bulldoze and deposit at their maximum extent.
Raising the temperature anomaly lifts the ELA, so a larger fraction of the glacier sits in the melt zone. Accumulation can no longer feed the lower tongue, the terminus retreats up-valley, length and volume fall, and the abandoned moraine marks where the ice front used to be.
The driving stress that deforms ice is ρg H sinα, which increases with slope angle α. Because flux scales with that stress cubed, even a modest steepening sharply boosts ice velocity, thins the glacier and pushes the terminus further down the valley before it reaches balance.
Most of the world's mountain glaciers are losing mass as warming raises their equilibrium lines, exactly the behaviour you can reproduce with the temperature slider. Their retreat affects sea level, alpine water supplies and the geological record of past ice ages, which makes glacier dynamics a key tool in glaciology and climate science.