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.

Description

Inclined slab ice exerts driving stress proportional to thickness and surface slope.

Inclined slab ice exerts driving stress proportional to thickness and surface slope. A valley shape factor modifies that local idealization.^[1]

Invert local shape-corrected slab driving stress for ice thickness; flat-slope inversions are undefined, and longitudinal stresses remain excluded.

When to use Thickness From Slope Driving Stress

Use this for the following task: Invert local shape-corrected slab driving stress for ice thickness; flat-slope inversions are undefined, and longitudinal stresses remain excluded.

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 Thickness From Slope Driving Stress 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 drivingStressPa, iceDensityKgPerM3, gravityMPerSecondSquared, surfaceSlopeDegrees, valleyShapeFactor using the field table, then run the tool.
Read inferredIceThicknessM. 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
drivingStressPa	Driving stress pa	number	Required
iceDensityKgPerM3	Ice density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required
surfaceSlopeDegrees	Surface slope degrees	number	Required
valleyShapeFactor	Valley shape factor	number	Required

Supply nonnegative driving stress, positive density/gravity and shape factor in (0,1]. Convert degrees to radians and require slope strictly between 0 and 90 degrees before inversion.^[2]

H = τ / (ρ g f sin(α))

This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.

Output field	Meaning	Value type
inferredIceThicknessM	Inferred ice thickness m	number

json

{
  "input": {
    "drivingStressPa": 450000,
    "iceDensityKgPerM3": 900,
    "gravityMPerSecondSquared": 10,
    "surfaceSlopeDegrees": 30,
    "valleyShapeFactor": 1
  },
  "output": {
    "inferredIceThicknessM": 100.00000000000001
  }
}

Limitations and assumptions

Flat slopes make this inversion undefined. Longitudinal stresses, sliding and bed geometry are not solved.

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 Shape Factor Valley Correction for this operation: 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.

Further background: Ice rheology.

References

Ice rheology — PISM
Thickness From Slope Driving Stress — 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.
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.