Glacial Flow Velocity Glens Law Calculator
Compute glacial flow velocity glen’s law using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
strain rate = A * tau^n; u_surface = 2A * tau^n * H / (n+1)
Where A = temperature-dependent flow parameter (Pa^-n s^-1), tau = basal shear stress = rho*g*H*sin(alpha), n = Glen exponent (typically 3), H = ice thickness, rho = ice density (917 kg/m3), g = gravity (9.81 m/s2), alpha = surface slope.
Worked Examples
Example 1: Alpine Valley Glacier Flow
Problem: A valley glacier has ice thickness of 200m, surface slope of 5 degrees, and ice temperature of -10C. Calculate the deformation velocity using Glen Flow Law with n=3.
Solution: Surface slope in radians: 5 x pi/180 = 0.0873 rad\nBasal shear stress: 917 x 9.81 x 200 x sin(0.0873) = 157,000 Pa = 157 kPa\nFlow parameter A at -10C: ~3.5 x 10^-25 Pa^-3 s^-1 (Arrhenius)\nSurface velocity = 2A x tau^n x H / (n+1)\n= 2 x 3.5e-25 x (157000)^3 x 200 / 4 = deformation velocity
Result: Basal stress: 157 kPa | Deformation velocity: ~15-25 m/yr typical for alpine glaciers
Example 2: Fast-Flowing Outlet Glacier
Problem: An outlet glacier has ice thickness of 1000m, surface slope of 1 degree, and near-melting temperature of -2C. How fast does it flow?
Solution: Basal shear stress: 917 x 9.81 x 1000 x sin(0.0175) = 157,200 Pa = 157 kPa\nFlow parameter A at -2C: much larger due to warm temperature\nWarm ice deforms 10-50x faster than cold ice\nAdding basal sliding at ~50% of deformation velocity\nTotal velocity likely 100-500 m/yr for outlet glaciers
Result: Stress similar to alpine glacier but warm ice flows much faster | Typical outlet: 100-1000 m/yr
Frequently Asked Questions
What is Glen Flow Law and how does it describe glacier movement?
Glen Flow Law, developed by John Glen in 1955, is the constitutive relationship that describes how ice deforms under applied stress. It states that the strain rate of ice is proportional to the applied stress raised to a power n, typically equal to 3. Mathematically, the strain rate epsilon equals A times tau to the power n, where A is a temperature-dependent flow parameter and tau is the applied shear stress. This nonlinear relationship means that doubling the stress increases the strain rate by a factor of eight when n equals 3. Glen Flow Law is the foundation of all modern glacier and ice sheet numerical models and remains one of the most important equations in glaciology.
What determines the flow parameter A in Glen Flow Law?
The flow parameter A, also called the creep parameter or rate factor, is primarily controlled by ice temperature through an Arrhenius-type relationship. A increases exponentially with temperature, meaning warmer ice deforms much more easily than cold ice. At -10 degrees Celsius, A is roughly ten times larger than at -30 degrees Celsius. Other factors that affect A include ice crystal fabric and orientation, impurity content, water content in temperate ice, and grain size. Ice with a strong preferred crystal orientation can flow up to ten times faster than randomly oriented ice. The presence of even small amounts of liquid water at grain boundaries in temperate glaciers dramatically increases A and enhances flow.
How does basal sliding contribute to glacier velocity?
Basal sliding occurs when the glacier slides over its bed, as opposed to internal deformation where ice crystals creep past each other. Sliding requires the base to be at the pressure melting point so that a thin water film or water-filled cavities can lubricate the interface. In temperate glaciers, basal sliding can account for 50 to 90 percent of the total surface velocity. In cold-based polar glaciers frozen to their beds, sliding is negligible and all motion comes from internal deformation. Basal sliding velocity depends on basal shear stress, bed roughness, and subglacial water pressure. High water pressure reduces the effective normal stress on the bed, dramatically increasing sliding speed, which is why glaciers often surge during periods of heavy meltwater input.
Why is the Glen Flow Law exponent n typically set to 3?
The value n equals 3 was determined experimentally by John Glen through laboratory creep tests on polycrystalline ice samples. This value has been broadly confirmed by field measurements and borehole deformation studies on numerous glaciers. The physical basis for n equals 3 is that ice deforms primarily through dislocation creep at the stress levels typical of glaciers, which is approximately 50 to 200 kilopascals. At very low stresses below about 10 kilopascals, diffusion creep dominates and n approaches 1, producing a linear viscous response. At very high stresses, n may increase above 3 as other deformation mechanisms activate. Some studies have suggested values between 2 and 4, and there is ongoing debate about whether n varies with stress level, temperature, and crystal fabric.
How do glaciologists measure glacier flow velocity in the field?
Modern glacier velocity measurements use several complementary techniques. GPS receivers placed on the glacier surface provide point measurements with millimeter precision at sub-daily temporal resolution, capturing both long-term flow and short-term velocity variations. Satellite remote sensing uses feature tracking between repeat images or interferometric synthetic aperture radar to map velocity fields across entire ice sheets. Borehole inclinometry measures the tilt of a borehole over time to determine the depth profile of deformation velocity. Historical methods include surveying stakes placed on the glacier surface. The combination of surface GPS, satellite data, and borehole measurements allows scientists to separate internal deformation from basal sliding and test the predictions of Glen Flow Law.
What is the difference between ice streams and regular glacier flow?
Ice streams are corridors of fast-flowing ice within an ice sheet that move at velocities of hundreds to thousands of meters per year, compared to the surrounding ice which moves at only a few meters per year. Ice streams typically flow 10 to 100 times faster than the adjacent slow-moving ice and drain the vast majority of ice from the Antarctic and Greenland ice sheets. Their fast flow is enabled by high basal sliding rates over deformable water-saturated sediments or hard bedrock lubricated by pressurized subglacial water. The margins of ice streams are marked by intense shear zones where ice deforms rapidly. Ice stream behavior can change dramatically over decades to centuries, with streams switching on and off, migrating laterally, and changing velocity.