<p>The content below is based on expressions found in <a href="https://en.wikipedia.org/wiki/Wind_gradient" rel="nofollow noreferrer">Wind gradient</a> from Wikipedia.  See that link for more background information.</p>
<p>Wind speed as a function of height can be modeled with the following expression:</p>
<p><span class="math-container">$$v_2 = v_1 \left(\frac{h_2}{h_1}\right)^a$$</span></p>
<p>Where <span class="math-container">$v_1$</span> and <span class="math-container">$v_2$</span> are the wind speeds are heights <span class="math-container">$h_1$</span> and <span class="math-container">$h_2$</span>, <span class="math-container">$a$</span> is a parameter related to the atmospheric stability.</p>
<p>Given your two values for wind speed at different height we want to solve for <span class="math-container">$a$</span>:</p>
<p><span class="math-container">$$a = \frac{\ln(v_2/v_1)}{\ln(h_2/h_1)}$$</span></p>
<p>You can now use this value, along with the original height / wind speed pairs to evaluate the wind speed at a different height.</p>
<p>The model will likely be best when the evaluated hight is between the points used to compute <span class="math-container">$a$</span>, basically interpolation will be better than extrapolation.</p>

CC BY-SA 4.0
2023-10-15T12:37:15.233Z
Thank you the explanation
fsumathdoc
CC BY-SA 4.0
2023-10-15T12:23:09.797Z
2023-10-15T12:23:09.797Z
GrapefruitIsAwesome
<p>If I have wind speeds at 80m and 120m above the surface and I am interested in approximating the speed at 100m, is it valid to just average the 80 and 120 speeds? In other words, should I expect wind speed to be a linear function of height or would a nonlinear function be more appropriate?</p>

<wind>
Interpolating Wind Speed
fsumathdoc
# Interpolating Wind Speed

(Asked by: username_0 on 2023-10-14)

If I have wind speeds at 80m and 120m above the surface and I am interested in approximating the speed at 100m, is it valid to just average the 80 and 120 speeds? In other words, should I expect wind speed to be a linear function of height or would a nonlinear function be more appropriate?

**Tags:** wind


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## 1 answers

### Answer by username_1 on 2023-10-15. Score: 1 | Accepted answer

The content below is based on expressions found in [Wind gradient](https://en.wikipedia.org/wiki/Wind_gradient) from Wikipedia. See that link for more background information.

Wind speed as a function of height can be modeled with the following expression:

$$v\_2 = v\_1 \left(\frac{h\_2}{h\_1}\right)^a$$

Where $v\_1$ and $v\_2$ are the wind speeds are heights $h\_1$ and $h\_2$, $a$ is a parameter related to the atmospheric stability.

Given your two values for wind speed at different height we want to solve for $a$:

$$a = \frac{\ln(v\_2/v\_1)}{\ln(h\_2/h\_1)}$$

You can now use this value, along with the original height / wind speed pairs to evaluate the wind speed at a different height.

The model will likely be best when the evaluated hight is between the points used to compute $a$, basically interpolation will be better than extrapolation.

> **Comments:**
> **username_0**: Thank you the explanation  

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