Presets
Playback
Climate (mass balance)
The ELA and the balance gradient set where ice builds up or melts away.
Ice physics
Warmer ice deforms faster; the enhancement factor stands in for sliding.
Bed
Mean slope and bumps of the rock under the glacier.
Time
Years of simulated time per real second.
Layers
Model checks
The science
How a glacier moves
Ice deforms under its own weight. In Glen’s flow law the shear strain rate grows with the cube of the stress, dε/dt = A τ^n with n = 3. In the shallow-ice approximation (valid because a glacier is thin compared with its length) the driving stress at the bed is τ = ρ g H |∂s/∂x|, where H is the ice thickness and s the surface elevation. Integrating the strain rate over the depth gives the velocity profile u(ζ) = 2A/(n+1) (ρ g)^n |s_x|^(n-1) (-s_x) [H^(n+1) - (H-ζ)^(n+1)] (ζ = height above the bed) and the depth-integrated flux q = 2A/(n+2) (ρ g)^n |s_x|^(n-1) (-s_x) H^(n+2). Thick ice on a steep surface moves very fast because of the powers 5 and 3.
Mass balance and the equilibrium line
Snow accumulates at high altitude and melts at low altitude. The model uses b(z) = min(b_max, β (z - ELA)) in metres of ice per year, so the equilibrium-line altitude (ELA) is where b = 0. Ice is conserved: ∂H/∂t = b - ∂q/∂x. The page solves this with an explicit conservative finite-volume scheme (100 cells of 200 m, a time step limited by the diffusive stability bound dt < 0.4 dx^2 / D) with no flux at the ice divide and free outflow at the valley end. A glacier is in balance when the integral of b along the flowline is zero; then the flux at each point equals the integral of the mass balance upstream (first graph).
Temperature, enhancement and the response time
The rate factor follows an Arrhenius law A(T) = A0 exp[-Q/R (1/T - 1/273.15)] with Q = 115 kJ/mol, so ice at -10 C flows about seven times slower than ice at 0 C. The enhancement slider multiplies the flux and stands in for basal sliding, which this model does not simulate separately. After a change in climate the glacier needs roughly H / b years (decades to centuries) to adjust, which is why the warming preset keeps losing ice long after the ELA stops rising.
Flow lines
The coloured markers are advected with the SIA horizontal velocity and with the vertical velocity from incompressibility, w = -∂Q/∂x at fixed height, where Q is the flux below that height. They sink in the accumulation zone and travel back to the surface in the ablation zone, which is how ice cores and debris emerge near the terminus.
Honest simplifications
One flowline (width is not tracked in the physics; the 3D valley only shows where the ice surface reaches the valley walls), isothermal ice with no heat transfer, no real basal sliding, no calving, no ice-sheet membrane stresses (longitudinal stresses are neglected, so the ice front is a smooth wedge), a fixed linear mass-balance profile and a bed with sinusoidal bumps. The shallow-ice approximation is poor near the ice divide and the terminus. The ice-age and warming presets are illustrations, not forecasts for a particular glacier.
What to try
- Choose the balanced alpine preset, wait for the glacier to settle (the graphs flatten) and then raise the ELA by 200 m: watch the volume graph decay with a time scale of centuries.
- Switch to the cold polar preset: the same thickness moves much more slowly (compare the surface speeds and the stress readout, which stays near 100 kPa).
- Run the warming preset and watch the terminus retreat uphill while the survey poles show the surface dropping.
- Set the bed undulation to 200 m: the surface speed varies along the flowline where the ice thickens over bed depressions.
- Compare the flux curve with the integral of the mass balance: they coincide only in a steady state.