Monin–Obukhov Length Calculator

Estimate atmospheric surface-layer stability from heat, momentum, moisture, direct length, or profile data, with unit conversions, validation, charts, and exportable calculation steps for analysis.


Sensible heat flux inputs

This convenient dry-atmosphere mode derives potential temperature and uses sensible heat flux.

kg/m³

Virtual potential temperature flux inputs

Use this mode when eddy-covariance or turbulence flux measurements are available.

K·m/s

Momentum-stress inputs

Friction velocity is derived from horizontal surface-stress components and air density.

Pa
Pa
kg/m³

Moist-air advanced inputs

This mode includes humidity and latent heat in the virtual potential temperature flux.

kg/m³
kg/kg

Direct conversion inputs

Enter L, 1/L, or z/L and derive the remaining stability quantities.

Wind and temperature profile inputs

This mode estimates stability from a bulk Richardson number. Use it only when flux measurements are unavailable.

Constants and advanced settings

m/s²
J/(kg·K)
J/kg

Scenario comparison

Compare dry sensible-heat cases. Values use SI units and upward-positive heat flux.

Nameu* (m/s)H (W/m²)Temperature (°C)Density (kg/m³)Height (m)L (m)z/LClassAction

CSV columns: name, uStar, heatFlux, temperatureC, density, height.

Sensitivity charts

Charts use the sensible heat-flux equation and current sensible-mode values.

Formula used

Virtual-flux form: L = −u*³θv ÷ (κg w′θv′).

Dry sensible-heat form: L = −ρcpθu*³ ÷ (κgH).

Dimensionless stability: ζ = z/L.

Stress-derived friction velocity: u* = √(|τ|/ρ).

How to use

  1. Select the calculation method matching your available measurements.
  2. Choose the heat-flux sign convention used by your dataset.
  3. Enter all measurements and confirm their displayed units.
  4. Open the constants panel only when nonstandard values are required.
  5. Submit the form and review stability, warnings, and calculation steps.
  6. Export results or compare additional dry sensible-heat scenarios.

Example data

Conditionu* (m/s)H (W/m²)TemperatureDensityHeightExpected sign
Sunny daytime0.3512025°C1.18 kg/m³10 mL negative
Clear nighttime0.20−3512°C1.23 kg/m³5 mL positive
Near-neutral windy0.65118°C1.21 kg/m³10 m|L| very large

Assumptions and limitations

Monin–Obukhov similarity is intended for the atmospheric surface layer. It assumes approximately stationary, horizontally homogeneous conditions over suitable terrain. Complex terrain, strong advection, rapid transitions, and very large stability magnitudes can reduce reliability.

The sensible heat mode treats thermal effects as dry buoyancy. Use moist-air mode when latent heat and humidity are important. Profile mode is an approximate screening method, not a replacement for measured turbulent fluxes.

Frequently asked questions

What does a negative Monin–Obukhov length mean?

A negative L generally indicates unstable, convective conditions. Upward buoyancy supports turbulence and vertical mixing.

What does a positive length mean?

A positive L indicates stable stratification. Buoyancy suppresses turbulent exchange and vertical motion.

Why is z/L more useful than L alone?

The stability parameter includes measurement height. It therefore expresses stability relative to the observation level.

What happens when heat flux equals zero?

The calculated length approaches infinity. Its reciprocal and z/L approach zero, representing neutral conditions.

Which calculation mode is most accurate?

The virtual potential temperature flux mode is preferred when reliable turbulence flux measurements are available.

Can friction velocity be calculated from stress?

Yes. The calculator combines stress components and applies u* = √(|τ|/ρ).

When should moist-air mode be used?

Use it when humidity and latent heat materially affect buoyancy, especially over wet or vegetated surfaces.

Why can profile mode differ from flux mode?

Profile estimates depend on empirical mappings and finite differences. Flux methods measure turbulent transport more directly.

Can the result be used over complex terrain?

Use caution. Slopes, buildings, coastlines, and roughness transitions can violate horizontal homogeneity assumptions.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.