Shear Strain Rate Depth

Estimate epsilon_xz=half du/dz with z positive upward from depths increasing downward and negligible dw/dx; distinct from along-flow normal strain or a constitutive Glen prediction.

Description

Vertical velocity shear contributes to tensor shear strain.

Vertical velocity shear contributes to tensor shear strain. With depth increasing downward and vertical coordinate positive upward, the velocity gradient changes sign.^[1]

Estimate epsilon_xz=half du/dz with z positive upward from depths increasing downward and negligible dw/dx; distinct from along-flow normal strain or a constitutive Glen prediction.

When to use Shear Strain Rate Depth

Use this for the following task: Estimate epsilon_xz=half du/dz with z positive upward from depths increasing downward and negligible dw/dx; distinct from along-flow normal strain or a constitutive Glen prediction.

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 Shear Strain Rate Depth 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 depthsBelowSurfaceM, horizontalVelocitiesMPerYear using the field table, then run the tool.
Read intervalTensorShearRatesPerYear. 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
depthsBelowSurfaceM	Depths below surface m	list of number; each entry: number	Required
horizontalVelocitiesMPerYear	Horizontal velocities m per year	list of number; each entry: number	Required

Pair horizontal velocities with strictly increasing nonnegative depths. Return one interval rate for each adjacent pair, using the factor of one half for tensor shear.^[2]

ε̇xz ≈ −Δu/(2Δdepth)

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

Output field	Meaning	Value type
intervalTensorShearRatesPerYear	Interval tensor shear rates per year	list of number

json

{
  "input": {
    "depthsBelowSurfaceM": [
      0,
      10,
      30
    ],
    "horizontalVelocitiesMPerYear": [
      20,
      10,
      0
    ]
  },
  "output": {
    "intervalTensorShearRatesPerYear": [
      0.5,
      0.25
    ]
  }
}

Limitations and assumptions

The approximation neglects the horizontal gradient of vertical velocity. It does not evaluate Glen’s law or along-flow normal strain.

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 Longitudinal Strain Rate for this operation: Estimate interval longitudinal normal strain rate from velocity gradients along a supplied flow transect; not transverse or tensor shear strain. For a complementary task, use Glen Flow Law Strain Rate for this operation: Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate.

Further background: Ice rheology.

References

Ice rheology — PISM
Shear Strain Rate Depth — tool.io

Similar or alternative tools

Longitudinal Strain Rate
Estimate interval longitudinal normal strain rate from velocity gradients along a supplied flow transect; not transverse or tensor shear strain.
Glen Flow Law Strain Rate
Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate.