Subglacial Flow Direction Gradient

Compute isotropic downhill hydraulic-potential direction from bed/thickness gradients and pressure ratio; flat gradients have no defined direction and anisotropic transmissivity is excluded.

Description

Subglacial water under an isotropic flow model moves down hydraulic potential.

Subglacial water under an isotropic flow model moves down hydraulic potential. Both bed elevation and ice overburden contribute to its gradient.^[1]

Compute isotropic downhill hydraulic-potential direction from bed/thickness gradients and pressure ratio; flat gradients have no defined direction and anisotropic transmissivity is excluded.

When to use Subglacial Flow Direction Gradient

Use this for the following task: Compute isotropic downhill hydraulic-potential direction from bed/thickness gradients and pressure ratio; flat gradients have no defined direction and anisotropic transmissivity is 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 Subglacial Flow Direction Gradient 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 bedElevationGradients, iceThicknessGradients, waterPressureOverburdenFraction, iceDensityKgPerM3, waterDensityKgPerM3, gravityMPerSecondSquared using the field table, then run the tool.
Read potentialGradientPaPerMeter, unitDownPotentialDirection. 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
bedElevationGradients	Bed elevation gradients	list of number; each entry: number	Required
iceThicknessGradients	Ice thickness gradients	list of number; each entry: number	Required
waterPressureOverburdenFraction	Water pressure overburden fraction	number	Required
iceDensityKgPerM3	Ice density kg per m3	number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Supply two horizontal components for each gradient, positive densities/gravity and a nonnegative pressure ratio. Reject a zero resultant gradient because its direction is undefined.^[2]

∇Φ = g(ρw∇b + fρi∇H); direction = −∇Φ/|∇Φ|

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

Output field	Meaning	Value type
potentialGradientPaPerMeter	Potential gradient pa per meter	list of number
unitDownPotentialDirection	Unit down potential direction	list of number

json

{
  "input": {
    "bedElevationGradients": [
      1,
      0
    ],
    "iceThicknessGradients": [
      0,
      1
    ],
    "waterPressureOverburdenFraction": 1,
    "iceDensityKgPerM3": 900,
    "waterDensityKgPerM3": 1000,
    "gravityMPerSecondSquared": 10
  },
  "output": {
    "potentialGradientPaPerMeter": [
      10000,
      9000
    ],
    "unitDownPotentialDirection": [
      -0.7432941462471662,
      -0.6689647316224496
    ]
  }
}

Limitations and assumptions

Coordinate axes and gradient units must agree. Anisotropic transmissivity and drainage-network routing are not modeled.

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 Hydraulic Potential Shreve for this operation: Evaluate Shreve hydraulic potential p_w+rho_w·g·bed elevation with caller water/overburden ratio; potentials share a vertical datum and no geodesy transform is performed. For a complementary task, use Effective Pressure Nye for this operation: Calculate signed ice-overburden minus subglacial water pressure and flag pressure above overburden; negative effective pressure is not clamped or interpreted as stable contact.

Further background: Subglacial hydrology.

References

Subglacial hydrology — PISM
Subglacial Flow Direction Gradient — tool.io

Similar or alternative tools

Hydraulic Potential Shreve
Evaluate Shreve hydraulic potential p_w+rho_w·g·bed elevation with caller water/overburden ratio; potentials share a vertical datum and no geodesy transform is performed.
Effective Pressure Nye
Calculate signed ice-overburden minus subglacial water pressure and flag pressure above overburden; negative effective pressure is not clamped or interpreted as stable contact.