Interpolating Wind Speed

Question

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?

Answer 1

The content below is based on expressions found in 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.