Shape Factor Valley Correction

Estimate valley shape factor A/(P·H) from a flat-surface piecewise-linear bed section; not inversion from basal stress or a universal valley correction.

Description

A valley shape factor relates cross-sectional area to the ice-contact perimeter and a characteristic thickness.

A valley shape factor relates cross-sectional area to the ice-contact perimeter and a characteristic thickness. It is a geometric correction for a simplified stress model.^[1]

Estimate valley shape factor A/(P·H) from a flat-surface piecewise-linear bed section; not inversion from basal stress or a universal valley correction.

When to use Shape Factor Valley Correction

Use this for the following task: Estimate valley shape factor A/(P·H) from a flat-surface piecewise-linear bed section; not inversion from basal stress or a universal valley correction.

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 Shape Factor Valley Correction 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 crossValleyCoordinatesM, iceThicknessesM, characteristicThicknessM using the field table, then run the tool.
Read crossSectionAreaM2, wettedBedPerimeterM, geometricShapeFactor. 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
crossValleyCoordinatesM	Cross valley coordinates m	list of number; each entry: number	Required
iceThicknessesM	Ice thicknesses m	list of number; each entry: number	Required
characteristicThicknessM	Characteristic thickness m	number	Required

Integrate a piecewise-linear thickness section by trapezoids. Require ordered coordinates and zero thickness at both edges, sum bed-segment lengths, and check the resulting factor lies in [0,1].^[2]

f = area/(wetted perimeter × characteristic H)

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
wettedBedPerimeterM	Wetted bed perimeter m	number
geometricShapeFactor	Geometric shape factor	number

json

{
  "input": {
    "crossValleyCoordinatesM": [
      -10,
      0,
      10
    ],
    "iceThicknessesM": [
      0,
      10,
      0
    ],
    "characteristicThicknessM": 10
  },
  "output": {
    "crossSectionAreaM2": 100,
    "wettedBedPerimeterM": 28.284271247461902,
    "geometricShapeFactor": 0.35355339059327373
  }
}

Limitations and assumptions

The surface is assumed flat. A characteristic thickness must be supplied; this is not a universal correction or stress inversion.

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 Basal Shear Stress for this operation: Calculate local slab driving and shape-corrected basal shear; longitudinal stress gradients and spatial force balance are excluded. For a complementary task, use Thickness From Slope Driving Stress for this operation: Invert local shape-corrected slab driving stress for ice thickness; flat-slope inversions are undefined, and longitudinal stresses remain excluded.

Further background: Ice rheology.

References

Ice rheology — PISM
Shape Factor Valley Correction — tool.io

Similar or alternative tools

Basal Shear Stress
Calculate local slab driving and shape-corrected basal shear; longitudinal stress gradients and spatial force balance are excluded.
Thickness From Slope Driving Stress
Invert local shape-corrected slab driving stress for ice thickness; flat-slope inversions are undefined, and longitudinal stresses remain excluded.