Monin–Obukhov Length Calculator

Calculator Inputs

Input method

Pick the data type available at your site.

Friction velocity, u* (m/s)

Derived from momentum flux measurements.

Virtual potential temperature, θv (K)

Use layer mean near the surface.

Kinematic virtual heat flux, w'θv' (K·m/s)

Positive usually indicates upward heat transport.

von Kármán constant, κ

Typical range is around 0.39–0.41.

Gravity, g (m/s²)

Use local value if you need extra precision.

Reference height, z (m)

Used to report the stability ratio z/L.

The Monin–Obukhov length links shear production to buoyancy in the surface layer. A common expression is:

L = − (u*³ · θv) / (κ · g · w'θv')

u* is friction velocity in meters per second.
θv is virtual potential temperature in kelvin.
w'θv' is kinematic virtual heat flux in K·m/s.
κ is the von Kármán constant, dimensionless.
g is gravitational acceleration in m/s².

If you only have sensible heat flux H, the calculator uses w'θ' = H/(ρ·cp) as an approximation for w'θv'.

Select an input method that matches your dataset.
Enter friction velocity and virtual potential temperature.
Provide kinematic flux, or enter sensible heat flux with air properties.
Optionally adjust κ, g, and the reference height z.
Press Calculate to view results above the form.
Use the CSV button for a data file export.
Use the PDF button for a printable report.

Case	u* (m/s)	θv (K)	H (W/m²)	ρ (kg/m³)	cp (J/kg·K)	L (m)	Interpretation
Daytime convection	0.35	302	200	1.18	1004	−43.1	Negative L, buoyancy supports turbulence.
Weakly stable evening	0.25	295	−30	1.22	1004	+75.9	Positive L, buoyancy suppresses turbulence.
Near-neutral windy	0.60	300	10	1.20	1004	−1670	Large \|L\|, shear dominates buoyancy.

The table is illustrative and may differ from site conventions.

1) Surface-Layer Stability and Why L Matters

The Monin–Obukhov length (L) is a stability scale for the atmospheric surface layer. It compares turbulence generated by wind shear with turbulence produced or suppressed by buoyancy. Knowing L helps you choose similarity corrections for near-surface wind and temperature profiles. It is also used to parameterize exchange of momentum, heat, and moisture in surface-flux models.

2) Physical Meaning of Positive and Negative L

The sign of L shows whether buoyancy enhances or damps turbulence. Negative L is typically unstable, convective conditions driven by surface heating. Positive L indicates stable stratification with reduced mixing. Very large |L| suggests near-neutral flow dominated by shear.

3) Inputs the Calculator Uses

This calculator accepts friction velocity (u*), virtual potential temperature (θv), and a heat-flux term. Enter kinematic virtual heat flux (w'θv') directly, or compute it from sensible heat flux (H), air density, and heat capacity. Optional κ, g, and reference height z support site conventions.

4) Typical Ranges and Quality Checks

In many field datasets, u* spans roughly 0.05–1.5 m/s and θv is often 250–330 K. Kinematic flux magnitudes are commonly below a few tenths of K·m/s, depending on season and surface type. If u* is near zero, L becomes unstable; if flux is near zero, |L| can become extremely large.

5) Interpreting z/L for Stability Classes

Many applications use the non-dimensional parameter z/L. Small |z/L| (for example, below about 0.05) is close to neutral. Negative z/L reflects unstable stratification, while positive values reflect stable stratification. Reporting z/L at your measurement height improves comparability.

6) When Virtual Flux Differs from Sensible Flux

Virtual terms include moisture effects that modify buoyancy. If you only have sensible heat flux, the calculator estimates kinematic flux using H/(ρ·cp). Where humidity is important, using directly measured virtual flux generally yields a more defensible L.

7) Practical Use in Dispersion and Flux-Gradient Work

Stability influences plume spread, eddy diffusivity, and surface exchange coefficients. With L and z/L, you can apply stability corrections to profiles and transfer relationships. Flux-gradient methods frequently rely on L to link observed gradients with turbulent fluxes.

8) Limitations and Good Practice Notes

Similarity theory works best over uniform terrain under quasi-steady conditions. Complex topography, sharp heterogeneity, and rapid transitions can violate assumptions. Document sensor height, averaging period, and flux processing choices so your reported L can be interpreted correctly.

1) What does a very large |L| mean?

It usually indicates near-neutral conditions where buoyancy effects are weak compared with shear, or where the heat-flux term is close to zero.

2) Why does L change sign?

The sign is controlled by the buoyancy flux term. Heating tends to make L negative (unstable), while cooling tends to make L positive (stable).

3) Which input is most sensitive?

Friction velocity and the heat-flux term both strongly affect L. Because u* is cubed, small errors in u* can create large changes in the result.

4) Can I use sensible heat flux instead of virtual flux?

Yes. The calculator can approximate kinematic flux from H using air density and heat capacity. Virtual flux is preferred when moisture significantly affects buoyancy.

5) What is z/L used for?

z/L is a standard stability parameter used in similarity functions and profile corrections. It helps compare stability across different heights and sites.

6) Why does the calculator show a warning near zero flux?

When the flux term approaches zero, the denominator becomes very small and L can become extremely large, making stability classification uncertain.

7) Is Monin–Obukhov theory valid everywhere?

It works best in the surface layer over uniform terrain under quasi-steady conditions. Strong heterogeneity, obstacles, or rapid transitions can reduce reliability.