Schmidt Stability Index

Compute signed Schmidt potential-energy stability from piecewise-constant layer areas/densities and depth-positive-down centers; negative values indicate an inverted profile, not positive mixing energy.

Description

Schmidt stability measures density stratification through potential energy per surface area.

Schmidt stability measures density stratification through potential energy per surface area. A signed calculation distinguishes stable density arrangement from an inverted column.^[1]

The tool returns schmidtStabilityJPerM2, volumeMeanDensityKgPerM3, volumeCentroidDepthM. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Schmidt Stability Index

Use this for the following task: Compute signed Schmidt potential-energy stability from piecewise-constant layer areas/densities and depth-positive-down centers; negative values indicate an inverted profile, not positive mixing energy. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Schmidt Stability Index and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter depthBoundariesM, layerAreasM2, layerDensitiesKgPerM3, gravityMPerSecondSquared according to the field table, then run the tool.
Read schmidtStabilityJPerM2, volumeMeanDensityKgPerM3, volumeCentroidDepthM. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
depthBoundariesM	Depth boundaries m	list of number	Required
layerAreasM2	Layer areas m2	list of number	Required
layerDensitiesKgPerM3	Layer densities kg per m3	list of number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Supply depth boundaries starting at zero and positive piecewise-constant layer areas and densities. Compute layer volumes, midpoint depths, volume-weighted means and the signed stability sum.

S=(g/surfaceArea)×Σvolume[i]×(centerDepth[i]−volumeCentroid)×(density[i]−volumeMeanDensity)

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
schmidtStabilityJPerM2	Schmidt stability j per m2	number
volumeMeanDensityKgPerM3	Volume mean density kg per m3	number
volumeCentroidDepthM	Volume centroid depth m	number

json

{
  "input": {
    "depthBoundariesM": [
      0,
      1,
      2
    ],
    "layerAreasM2": [
      10,
      10
    ],
    "layerDensitiesKgPerM3": [
      1000,
      1002
    ],
    "gravityMPerSecondSquared": 10
  },
  "output": {
    "schmidtStabilityJPerM2": 10,
    "volumeMeanDensityKgPerM3": 1001,
    "volumeCentroidDepthM": 1
  }
}

Limitations and assumptions

Each layer area is constant here rather than a contour interpolation. Negative stability remains negative; it is not reported as a positive energy requirement for mixing.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Lake Number Inertial when you need its operation: Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold. Choose Density Gradient Stratification Strength for the complementary operation: Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

Lake Physics Tools: rLakeAnalyzer reference manual — Winslow, Read and colleagues; GLEON

Similar or alternative tools

Lake Number Inertial
Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold.
Density Gradient Stratification Strength
Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency.