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.

Description

Buoyancy frequency squared describes the strength and sign of a density gradient.

Buoyancy frequency squared describes the strength and sign of a density gradient. With depth positive downward, density increasing downward gives positive N².^[1]

The tool returns signedBuoyancyFrequencySquaredPerSecondSquared, stableIntervalFlags. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Density Gradient Stratification Strength

Use this for the following task: Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Density Gradient Stratification Strength and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter depthsM, densitiesKgPerM3, referenceDensityKgPerM3, gravityMPerSecondSquared according to the field table, then run the tool.
Read signedBuoyancyFrequencySquaredPerSecondSquared, stableIntervalFlags. 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
depthsM	Depths m	list of number	Required
densitiesKgPerM3	Densities kg per m3	list of number	Required
referenceDensityKgPerM3	Reference density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Supply increasing nonnegative depths, aligned positive densities and positive reference density and gravity. Return signed interval N² values and numeric stable flags for values strictly above zero.

N²[i]=(gravity/referenceDensity)×(density[i+1]−density[i])/(depth[i+1]−depth[i])

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

Output field	Meaning	Value type
signedBuoyancyFrequencySquaredPerSecondSquared	Signed buoyancy frequency squared per second squared	list of number
stableIntervalFlags	Stable interval flags	list of number

json

{
  "input": {
    "depthsM": [
      0,
      10,
      20
    ],
    "densitiesKgPerM3": [
      1000,
      1002,
      1001
    ],
    "referenceDensityKgPerM3": 1000,
    "gravityMPerSecondSquared": 10
  },
  "output": {
    "signedBuoyancyFrequencySquaredPerSecondSquared": [
      0.002,
      -0.001
    ],
    "stableIntervalFlags": [
      1,
      0
    ]
  }
}

Limitations and assumptions

Negative values remain instability indicators; no real square-root frequency is invented. Sampling resolution, salinity effects and measurement uncertainty are external.

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 Fall Turnover Density Inversion Trigger when you need its operation: Screen resolved down-column density inversions against caller measurement tolerance; inversion is a mixing trigger screen, not proof of complete fall turnover. Choose Richardson Number Water Column for the complementary operation: Compute signed bulk Richardson number for a supplied shear-layer scale and density contrast; density inversion remains negative and no critical instability diagnosis is imposed.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

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

Similar or alternative tools

Fall Turnover Density Inversion Trigger
Screen resolved down-column density inversions against caller measurement tolerance; inversion is a mixing trigger screen, not proof of complete fall turnover.
Richardson Number Water Column
Compute signed bulk Richardson number for a supplied shear-layer scale and density contrast; density inversion remains negative and no critical instability diagnosis is imposed.