The temporalBehaviour() and the
spatialBehaviour() functions allow computing wind speed and
direction along the lifespan of a tropical cyclone. The
temporalBehaviour() function focuses on the temporal
variation at a specific location while the
spatialBehaviour() function focuses on the spatial
variation over a given area. Both functions also allow to compute
summary statistics about the behaviour of the wind generated by
cyclones. Three summary statistics are available: maximum sustained wind
speed, power dissipation index, and the duration of exposure to winds
reaching defined speed thresholds.
The maximum sustained wind speed (MSW, in \(m.s^{-1}\)) over the lifespan of a storm is computed as follows:
\[ \max(v(t) | t \in [0,T]) \]
where \(t\) is the time of the
observation
\(T\) is the lifespan
of the storm
The power dissipation index (PDI, in \(J.m^{2}\)) or total power dissipated by a tropical storm over its lifespan (Emanuel 1999, 2005) is computed as follows:
\[ \int_T \rho \times C_d \times v_r^3 \ dt \]
where \(t\) is the time of the
observation
\(T\) is the lifespan
of the storm
\(\rho\) is the air
density fixed to \(1\) \(kg.m^{-3}\) as in Emanuel (1999)
\(C_d\) is the drag coefficient of the storm
fixed to \(2\) X \(10^{-3}\) as in Emanuel (1999)
The duration of exposure (in \(hours\)) to winds reaching defined speed thresholds is computed as follows:
\[ \int_T c(v_t) dt \]
\[ \left\{ \begin{aligned} c(v_t) &= 1 \quad if \quad v_t \geq Thd\\ c(v_t) &= 0 \quad if \quad v_t < Thd\\ \end{aligned} \right. \]
where
\(t\) is the time of the
observation
\(T\) is the lifespan
of the storm
\(v_t\) is the
maximum sustained wind speed at time \(t\) (in \(m.s^{-1}\))
\(Thd\) is the minimum wind sped threshold
(in \(m.s^{-1}\))
By default the duration of exposure is computed for each
Saffir-Simpson Hurricane Scale threshold values for tropical cyclone
categories (i.e., \(33\), \(43\), \(50\) ,\(58\), and \(70\) \(m.s^{-1}\), (Simpson
1974)) but can be defined using the wind_threshold
argument.