Steady State Thickness Profile Vialov

Evaluate ideal Vialov flat-bed, no-sliding, isothermal Glen-flow half-dome with uniform ice-equivalent accumulation and zero terminus thickness; no bed geometry or transient dynamics.

Description

An ideal Vialov profile describes a steady ice half-dome on a flat bed.

An ideal Vialov profile describes a steady ice half-dome on a flat bed. Uniform accumulation balances deformation flux with no basal sliding.^[1]

Evaluate ideal Vialov flat-bed, no-sliding, isothermal Glen-flow half-dome with uniform ice-equivalent accumulation and zero terminus thickness; no bed geometry or transient dynamics.

When to use Steady State Thickness Profile Vialov

Use this for the following task: Evaluate ideal Vialov flat-bed, no-sliding, isothermal Glen-flow half-dome with uniform ice-equivalent accumulation and zero terminus thickness; no bed geometry or transient dynamics.

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 Steady State Thickness Profile Vialov 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 distancesFromDivideM, halfLengthM, uniformAccumulationMetersIcePerYear, glenExponent, rateFactorPerYearPaToMinusN, iceDensityKgPerM3, gravityMPerSecondSquared using the field table, then run the tool.
Read steadyThicknessesM. 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
distancesFromDivideM	Distances from divide m	list of number; each entry: number	Required
halfLengthM	Half length m	number	Required
uniformAccumulationMetersIcePerYear	Uniform accumulation meters ice per year	number	Required
glenExponent	Glen exponent	number	Required
rateFactorPerYearPaToMinusN	Rate factor per year pa to minus n	number	Required
iceDensityKgPerM3	Ice density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Require positive model constants, 0 < n ≤ 5 and nonempty positions in [0,L]. Evaluate the profile independently at each distance from the divide; the terminus at L has zero thickness.^[2]

c = 2A(ρg)^n/(n+2); H(x) = [2(a/c)^(1/n)(L^((n+1)/n) − x^((n+1)/n))]^(n/(2n+2))

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

Output field	Meaning	Value type
steadyThicknessesM	Steady thicknesses m	list of number

json

{
  "input": {
    "distancesFromDivideM": [
      0,
      1,
      2
    ],
    "halfLengthM": 2,
    "uniformAccumulationMetersIcePerYear": 1,
    "glenExponent": 1,
    "rateFactorPerYearPaToMinusN": 1,
    "iceDensityKgPerM3": 1,
    "gravityMPerSecondSquared": 1
  },
  "output": {
    "steadyThicknessesM": [
      1.8612097182041991,
      1.7320508075688772,
      0
    ]
  }
}

Limitations and assumptions

Flat bed, isothermal rate factor, uniform ice-equivalent accumulation and steady no-sliding flow are imposed assumptions.

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 Plastic Ideal Yield Stress for this operation: Compute an ideal perfectly plastic flat-bed thickness profile H²=2·tau_y·x/(rho·g); not a Glen steady-state dome or yield-strength determination. 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: Solving the Vialov equation of glaciology in terms of elementary functions.

References

Solving the Vialov equation of glaciology in terms of elementary functions — Valerio Faraoni, arXiv
Steady State Thickness Profile Vialov — tool.io

Similar or alternative tools

Plastic Ideal Yield Stress
Compute an ideal perfectly plastic flat-bed thickness profile H²=2·tau_y·x/(rho·g); not a Glen steady-state dome or yield-strength determination.
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.