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.
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.