The Front Area Index (FAI) is often incorrectly set by ordinary users due to unconscious omission, while heights and surface coverage fractions are usually properly set.
Here we introduce a simple method for deriving FAI ($\lambda_f$) based on morphological parameters such as height $h$, surface coverage fraction (effectively Plan Area Index or PAI, $\lambda_p$), and surface area $A$. We make different assumptions for various roughness element land covers:
Buildings
Assuming all buildings are square cuboids with height $h$:
For $N$ cylindrical trees with porosity $P$, height $h$, radius $r$, frontal area $A_f$, and plan area $A_p$: considering only the crown,
$$
\begin{aligned}
& Af = 2 h{crown} r_{crown} N(1-P) \
& N = Ap / (\pi r{crown}^2) \
& Af = 2 h{crown} r_{crown}(1-P) Ap / (\pi r{crown}^2) \
& \lambdaf = 2 h{crown}(1-P)\lambdap / (\pi r{crown})
\end{aligned}
$$
Evergreen Trees
According to Lai et al. (2022), for evergreen trees, the values are approximately $P = 0.32$, $h{crown} = 0.65h$, and $r{crown} = 0.25h$. Therefore, we can calculate $\lambda_f$ as follows:
The sections related to trees are contributed by @XiaoxiongXie.
Lai et al. (2022): Lai, C., Feng, J., Wang, L., Zhang, Y., Sun, Y., Chen, X. and Guo, W. (2022). Evaluating the Wind Load Towards the Crown Features on 7 Evergreen Species by Wind Tunnel Experiments. Available at SSRN: https://ssrn.com/abstract=4058842 or http://dx.doi.org/10.2139/ssrn.4058842
The Front Area Index (FAI) is often incorrectly set by ordinary users due to unconscious omission, while heights and surface coverage fractions are usually properly set.
Here we introduce a simple method for deriving FAI ($\lambda_f$) based on morphological parameters such as height $h$, surface coverage fraction (effectively Plan Area Index or PAI, $\lambda_p$), and surface area $A$. We make different assumptions for various roughness element land covers:
Buildings
Assuming all buildings are square cuboids with height $h$:
$$ \begin{aligned} l_h &= \sqrt{A * \lambda_p} \ \lambda_f &= \frac{l_h h}{A} = \sqrt{\frac{\lambda_p}{A}}h \end{aligned} $$
Trees
For $N$ cylindrical trees with porosity $P$, height $h$, radius $r$, frontal area $A_f$, and plan area $A_p$: considering only the crown,
$$ \begin{aligned} & Af = 2 h{crown} r_{crown} N(1-P) \ & N = Ap / (\pi r{crown}^2) \ & Af = 2 h{crown} r_{crown}(1-P) Ap / (\pi r{crown}^2) \ & \lambdaf = 2 h{crown}(1-P)\lambdap / (\pi r{crown}) \end{aligned} $$
Evergreen Trees
According to Lai et al. (2022), for evergreen trees, the values are approximately $P = 0.32$, $h{crown} = 0.65h$, and $r{crown} = 0.25h$. Therefore, we can calculate $\lambda_f$ as follows:
$$ \lambda_f = \frac{\lambda_p(2 0.65 0.68)}{0.25 * \pi} = 1.07 \lambda_p $$
Deciduous Trees
For simplicity, we use the same assumptions for deciduous trees as for evergreen ones but the SUEWS calculated porosity, we can have
$$ \lambda_f = \frac{\lambda_p(2 0.65 (1-P))}{0.25 * \pi} = 1.66 (1-P) \lambda_p $$
Acknowledgements