API wind spectrum

The API spectrum representing typhoon wind conditions may be written

\[S(f, z) = \frac{\sigma(z)^2}{f_p(1+1.5\frac{f}{f_p})^{5/3}}\]

where

\[f_p = \frac{\beta \bar{u}(z)}{z} \label{eq-api-2}\]

\[\sigma(z) = \begin{cases} 0.15 \bar{u}(z) \left( \displaystyle \frac{z}{z_s} \right)^{-0.125}, & z \leq z_s \\ \\ 0.15 \bar{u}(z) \left( \displaystyle \frac{z}{z_s} \right)^{-0.275}, & z > z_s \end{cases} \label{eq-api-3}\]

and

\(\beta\)

frequency parameter (default value is \(0.025\))

\(z_s\)

thickness of surface layer