# Chapter 23 Wind extinction

In this chapter we describe a few wind extinction models that are implemented in medfate. Wind extinction is rellevant: (a) to determine convective heat exchanges between the soil and the canopy; (b) to estimate wind speed and energy balance at the leaf level for different plant cohorts; and (c) for fire behaviour calculations.

## 23.1 Wind speed at the top of the canopy

Input wind speed ($$u$$) is assumed to represent the speed of wind at 6 m (20 feet) above the canopy. Following Albini & Baughman (1979) the wind speed (in $$m·s^{-1}$$) at the top of the canopy is:

$$$u_{top} = \frac{(1.01857\cdot u) \cdot 0.4265092 \cdot H_{canopy}}{log(20 + 1.181102 \cdot H_{top})}$$$ where $$H_{top}$$ is the canopy top height in $$m$$.

## 23.2 Wind extinction profile

The wind extinction profile, i.e the wind speed at any height $$z$$ in $$m$$, can be calculated following Massman (1987):

$\begin{eqnarray} \beta_{stand} &=& \frac{4.0 \cdot 0.2 \cdot LAI_{stand}^{phi}}{0.16 \cdot 1.5^2} \\ u(z) &=& u_{top} \cdot \sqrt{\frac{\cosh(\beta_{stand} \cdot z / H_{top})}{\cosh(\beta_{stand})}} \end{eqnarray}$

### Bibliography

Albini, F. & Baughman, R. (1979). Estimating windspeeds for predicting wildland fire behavior. USDA Forest Service, Intermountain Forest and Range Experiment Station, Research Paper, INT-RP-221.
Massman, W. (1987). A comparative study of some mathematical models of the mean wind structure and aerodynamic drag of plant canopies. Boundary-Layer Meteorology, 40, 179–197.