Parabolic Channel Discharge
Analytically integrate local slab Glen flux over a parabolic thickness section plus uniform sliding; excludes lateral stress coupling and uses stress-gradient units Pa/m.
Description
A parabolic ice cross section varies in thickness across its width.
A parabolic ice cross section varies in thickness across its width. Integrating a local Glen slab flux separates deformation from uniform sliding.1
Analytically integrate local slab Glen flux over a parabolic thickness section plus uniform sliding; excludes lateral stress coupling and uses stress-gradient units Pa/m.
When to use Parabolic Channel Discharge
Use this for the following task: Analytically integrate local slab Glen flux over a parabolic thickness section plus uniform sliding; excludes lateral stress coupling and uses stress-gradient units Pa/m.
Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
How to use Parabolic Channel Discharge and understand its results
- Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
- Enter halfWidthM, centerThicknessM, glenExponent, rateFactorPerYearPaToMinusN, drivingStressGradientPaPerMeter, uniformSlidingVelocityMPerYear using the field table, then run the tool.
- Read crossSectionAreaM2, deformationFluxM3PerYear, slidingFluxM3PerYear, totalFluxM3PerYear. Interpret flags, units, ordering and placeholder values using the rules below.
- Review any reported issue or failed check, correct the supplied values when appropriate, and verify the result in its intended context.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| halfWidthM | Half width m | number | Required |
| centerThicknessM | Center thickness m | number | Required |
| glenExponent | Glen exponent | integer | Required |
| rateFactorPerYearPaToMinusN | Rate factor per year pa to minus n | number | Required |
| drivingStressGradientPaPerMeter | Driving stress gradient pa per meter | number | Required |
| uniformSlidingVelocityMPerYear | Uniform sliding velocity m per year | number | Required |
Supply half-width W, central thickness H and stress gradient G in Pa/m. Require integer n from 1 to 5. Use a stable product for the parabolic integral, then add sliding flux.2
area = 4WH/3; Qdef = [2A/(n+2)]G^n H^(n+2)·2W·Π(k=1..n+2)2k/(2k+1); Qslide = area u This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.
| Output field | Meaning | Value type |
|---|---|---|
| crossSectionAreaM2 | Cross section area m2 | number |
| deformationFluxM3PerYear | Deformation flux m3 per year | number |
| slidingFluxM3PerYear | Sliding flux m3 per year | number |
| totalFluxM3PerYear | Total flux m3 per year | number |
{
"input": {
"halfWidthM": 1,
"centerThicknessM": 1,
"glenExponent": 1,
"rateFactorPerYearPaToMinusN": 1,
"drivingStressGradientPaPerMeter": 1,
"uniformSlidingVelocityMPerYear": 0
},
"output": {
"crossSectionAreaM2": 1.3333333333333333,
"deformationFluxM3PerYear": 0.6095238095238095,
"slidingFluxM3PerYear": 0,
"totalFluxM3PerYear": 0.6095238095238095
}
}Limitations and assumptions
Lateral stress coupling is excluded. The rate factor must use years and the chosen exponent; the section is idealized.
Constants and empirical coefficients are supplied rather than calibrated. Check units and observational applicability before interpreting the model. Malformed requests produce input errors. A successfully evaluated request can still contain false flags, empty result lists or a result outside the supplied threshold; those outcomes have the meanings stated above.
Alternative or Complementary methods
Choose Newtonian Slab Flow Rate for this operation: Evaluate constant-viscosity inclined-slab deformation from supplied maximum basal shear stress; excludes basal sliding. For a complementary task, use Flux Gate Discharge for this operation: Integrate signed normal ice flux over supplied gate strips with depth-mean/surface velocity calibration; widths are physical section measurements, not geodesy coordinates.
Further background: Ice rheology.
References
-
Ice rheology — PISM
-
Parabolic Channel Discharge — tool.io
Similar or alternative tools
- Newtonian Slab Flow Rate
Evaluate constant-viscosity inclined-slab deformation from supplied maximum basal shear stress; excludes basal sliding.
- Flux Gate Discharge
Integrate signed normal ice flux over supplied gate strips with depth-mean/surface velocity calibration; widths are physical section measurements, not geodesy coordinates.