Behaviour

2024-10-24

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.

Maximum sustained wind speed

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

Power Dissipation Index

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)

Duration of exposure

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.

References

Emanuel, Kerry A. 1999. “The Power of a Hurricane: An Example of Reckless Driving on the Information Superhighway.” Weather 54 (4): 107–8. https://doi.org/10.1002/j.1477-8696.1999.tb06435.x.

———. 2005. “Increasing Destructiveness of Tropical Cyclones over the Past 30 Years.” Nature 436 (7051): 686–88. https://doi.org/10.1038/nature03906.

Simpson, R. H. 1974. “The Hurricane Disaster—Potential Scale.” Weatherwise, July. https://doi.org/10.1080/00431672.1974.9931702.