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_power_1999; @emanuel_increasing_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_power_1999

$C_d$ is the drag coefficient of the storm fixed to $2$ X $10^{-3}$ as in @emanuel_power_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_hurricane_2010]) but can be defined using the `wind_threshold`

argument.

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