Calculator
Formula Used
The logarithmic wind profile describes the mean wind speed within the surface layer. For neutral conditions (no stability correction), the profile can be written as:
If you have a measured reference wind speed Uref at height zref, a practical ratio form is:
When stability is enabled, a momentum correction term ψm is applied:
Use stability only when you can estimate L. Otherwise, neutral is the safer assumption.
How to Use This Calculator
- Choose Calculation mode based on your available measurements.
- Enter the target height z, roughness length z0, and optional displacement height d.
- For reference mode, provide Uref and zref. For friction mode, provide u*.
- Enable stability only if you know the sign and magnitude of L.
- Press Calculate to see results above the form, then export if needed.
Example Data Table
Sample inputs and expected trends for neutral conditions.
| Terrain | z0 (m) | Uref (m/s) | zref (m) | Target z (m) | Typical U(z) behavior |
|---|---|---|---|---|---|
| Open water | 0.0002 | 6.0 | 10 | 50 | Strong increase with height; low drag. |
| Short grass | 0.03 | 5.0 | 10 | 30 | Moderate increase with height; common sites. |
| Urban | 0.50 | 4.0 | 10 | 60 | Slower near ground; large shear aloft. |
Log Wind Profile Guide
1) Why the log profile matters
Near the ground, wind speed increases rapidly with height because surface drag slows the air. The logarithmic wind profile is a standard way to estimate mean wind in the atmospheric surface layer, supporting wind-energy screening, dispersion studies, and sensor siting.
2) Key inputs and what they represent
The calculator uses height z, roughness length z0, and optional displacement height d. Roughness length summarizes terrain drag: open water can be about 0.0002 m, short grass around 0.03 m, and dense urban areas near 0.5 m.
3) Reference-speed mode for practical field data
If you have a mast measurement, reference mode scales wind from zref to z using the ratio of logarithmic terms. For example, with Uref = 5 m/s at zref = 10 m over grass (z0 = 0.03 m), the predicted speed at z = 30 m increases because ln((z−d)/z0) grows with height.
4) Friction-velocity mode for advanced studies
When turbulence measurements provide friction velocity u*, the calculator can compute U(z) directly. Typical daytime surface-layer values often fall between 0.2 and 0.6 m/s, depending on terrain and mixing. The default Von Kármán constant is κ = 0.41.
5) Stability correction using Monin–Obukhov length
Stability changes vertical shear. If you know Monin–Obukhov length L, enabling correction applies the momentum function ψm. Negative L represents unstable, convective conditions, which typically reduce shear, while positive L indicates stable stratification, often increasing shear.
6) Displacement height for canopies and cities
Displacement height d shifts the effective origin of the wind profile and is important above tall vegetation or dense obstacles. A common engineering approximation is d ≈ 0.6–0.8 of canopy height, but local guidance or measurements are best.
7) Data quality and typical use ranges
The log profile is most reliable within the surface layer and above the roughness sublayer. Ensure z − d is larger than z0, and avoid using the method too close to obstacles. If heights are only a few meters in urban terrain, uncertainty can be large.
8) Reporting and exporting results
For professional reporting, export the inputs and computed outputs to CSV or PDF. Include the chosen terrain parameters, stability setting, and units. Documenting z0, d, and whether ψm was applied makes comparisons across sites and campaigns consistent.
FAQs
1) What is roughness length z0?
It is a terrain parameter that summarizes surface drag in the log profile. Smaller values represent smoother surfaces like water, while larger values represent rougher terrain such as forests or cities.
2) When should I use displacement height d?
Use d when wind flows over tall canopies or dense obstacles. It shifts the profile upward to reflect that momentum exchange occurs above the surface. For open terrain, set d = 0.
3) Do I need stability correction for every case?
Not always. If you do not have a reliable estimate of Monin–Obukhov length L, neutral is a sensible default. Stability correction helps when your project requires higher accuracy and you know atmospheric conditions.
4) Why does my result change a lot when z0 changes?
The log term ln((z−d)/z0) is sensitive to z0. Rougher terrain increases drag, lowering wind near the surface and changing the shear with height. Pick z0 from credible site data.
5) Can I estimate friction velocity from a reference speed?
Yes. In reference mode the calculator reports an estimated u* based on your Uref, heights, and stability setting. Treat it as an inference, not a direct measurement.
6) What heights are typical for wind-energy screening?
Many studies scale from a 10 m measurement to hub heights like 60–120 m. Use appropriate z0 and consider stability if you need finer accuracy, especially for nocturnal stable periods.
7) Why does the calculator require z greater than d?
The model uses effective height z − d. If z ≤ d, the effective height is zero or negative, which breaks the logarithm and no physical mean profile can be computed.