Aerodynamic Roughness Length Calculator

Estimate roughness from wind, displacement, and canopy geometry. Compare modes with graphs, exports, and worked examples. Useful for micrometeorology, dispersion studies, and boundary-layer planning.

Calculator Inputs

Choose a solving mode. The calculator supports single-height wind inversion, two-height wind profile fitting, and canopy-based estimation with a reference wind.

Switch modes to solve roughness length from different field situations.
Use 0.41 for most neutral atmospheric surface-layer applications.
This fills realistic test values so you can inspect outputs quickly.
Wind speed measured at one known height.
Height of the anemometer above the ground.
Often obtained from turbulence or eddy covariance data.
Use zero for smooth ground with negligible tall obstacles.
Wind speed at the lower observation height.
Lower mast height or sensor height.
Wind speed at the upper observation height.
Upper mast height or sensor height.
Estimate this from canopy or obstacle geometry when needed.
Representative mean obstacle or canopy height.
Common starting estimate: 0.60 to 0.75.
Common starting estimate: 0.08 to 0.20.
Measured wind speed above the canopy or obstacle field.
Must be above displacement height and sufficiently above z0.

Formula Used

1) Neutral logarithmic wind profile

The core surface-layer relationship is U(z) = (u* / k) × ln((z - d) / z0).

Here U(z) is wind speed at height z, u* is friction velocity, k is the von Kármán constant, d is displacement height, and z0 is aerodynamic roughness length.

2) Single-height inversion

If wind speed, friction velocity, and displacement height are known, roughness length is found from z0 = (z - d) / exp((k × U) / u*).

3) Two-height inversion

First compute u*/k = (U2 - U1) / ln((z2 - d)/(z1 - d)).

Then calculate z0 = (z1 - d) / exp(U1 / (u*/k)). This mode is useful when friction velocity was not measured directly.

4) Canopy estimate mode

This mode estimates displacement and roughness from obstacle height: d = λd × h and z0 = λz0 × h.

It then derives friction velocity using the reference wind: u* = (k × Uref) / ln((zref - d)/z0).

How to Use This Calculator

Step 1: Select the solving mode that matches your field data.

Step 2: Enter heights in meters and wind speeds in meters per second.

Step 3: Keep the von Kármán constant at 0.41 unless your method requires another value.

Step 4: Add displacement height when vegetation, buildings, or dense obstacles shift the zero-plane upward.

Step 5: Click the calculate button to show the result section above the form.

Step 6: Review the computed roughness length, wind-profile graph, terrain class, and export files if needed.

Example Data Table

These sample rows show realistic starting points for testing the calculator. Exact values vary with atmospheric stability, fetch, and terrain uniformity.

Mode Sample inputs Approx. output Likely terrain meaning
Single-height U = 6.2 m/s, z = 10 m, u* = 0.42 m/s, d = 0 m z0 ≈ 0.023 m Open terrain with low vegetation
Two-height U1 = 3.8 m/s at 4 m, U2 = 5.6 m/s at 12 m, d = 0.8 m z0 ≈ 0.127 m Tall crops or rough open land
Canopy estimate h = 12 m, λd = 0.67, λz0 = 0.12, Uref = 5.4 m/s at 20 m z0 = 1.44 m Dense canopy or urban-like drag

Frequently Asked Questions

1) What is aerodynamic roughness length?

It is a parameter that represents how strongly a surface slows airflow. Larger values indicate rougher terrain, stronger drag, and a steeper near-surface wind gradient.

2) Is roughness length the same as obstacle height?

No. Roughness length is not a physical height of an object. It is a modeled parameter inferred from the wind profile and depends on terrain texture, obstacle spacing, and canopy structure.

3) When should I use displacement height?

Use displacement height when tall crops, trees, or buildings shift the effective origin of the wind profile upward. For very smooth or short surfaces, displacement height is often close to zero.

4) Why does the calculator assume a logarithmic profile?

The neutral logarithmic profile is the standard first model for the atmospheric surface layer. It is widely used when stability corrections are unavailable or when a quick neutral approximation is acceptable.

5) Can I use this for unstable or stable atmospheric conditions?

Use caution. This calculator is designed for neutral-profile estimation. Strongly stable or unstable conditions can change the profile shape, so Monin–Obukhov stability corrections may be needed.

6) What does a very small z0 value mean?

A very small roughness length suggests a smooth surface such as water, snow, or flat bare soil. These surfaces generate less drag and permit faster wind close to the ground.

7) Why might my dual-height calculation fail?

It usually fails when the two measurements do not create a positive logarithmic slope, the chosen displacement height is too large, or the wind speeds were recorded under inconsistent conditions.

8) How should I interpret the graph?

The graph plots modeled wind speed against height. A rougher surface generally shifts the curve, showing slower air near the surface and stronger speed increase with height.

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